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NCERT Solutions for Class 12 Maths Chapter 13 Probability are provided here. You have already studied the basics of probability class 12 in our previous classes like probability as a measure of uncertainty of events in a random experiment, addition rule of probability etc. NCERT solutions for class 12 maths chapter 13 probability will build your base to study probability theory in higher studies therefore probability class 12 ncert solutions become very important.
NCERT Class 12 Maths Chapter 13 solutions include concepts of discrete probability, computational probability and stochastic process. The important topics like conditional probability, Bayes' theorem, multiplication rule of probability, and independence of events are covered in this chapter of NCERT Class 12 maths probability books. Questions from all these topics are covered in NCERT solutions for class 12 maths chapter 13 probability.
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Also, you will learn some important concepts of the random variable, probability distribution, and the mean and variance of a probability distribution in this chapter 13 NCERT Class 12 maths solutions PDF. class 12 maths ncert solutions pdf will help you to learn the concept of probability distribution which will be required in higher study. NCERT solutions help students to understan the concepts in a much easy way. Here you will get NCERT solutions for class 12 other subjects also.
Also read:
>> Conditional Probability: Conditional probability is the likelihood of an event occurring based on the occurrence of a preceding event. For two events A and B with the same sample space, the conditional probability of event A given that B has occurred (P(A|B)) is defined as:
P(A|B) = P(A ∩ B) / P(B) (when P(B) ≠ 0)
Other conditional probability relationships:
P(S|F) = P(F|F) = 1
P((A ∪ B)|F) = P(A|F) + P(B|F) – P((A ∩ B)|F)
P(E'|F) = 1 − P(E|F)
>> Multiplication Rule: The multiplication rule relates the probability of two events E and F in a sample space S:
P(E ∩ F) = P(E) P(F|E) = P(F) P(E|F) (when P(E) ≠ 0 and P(F) ≠ 0)
>> Independent Events: Two experiments are considered independent if the probability of the events E and F occurring simultaneously is the product of their individual probabilities:
P(E ∩ F) = P(E) * P(F)
>> Bayes’ Theorem: Bayes’ theorem deals with events E1, E2, …, En that form a partition of the sample space S. It allows the calculation of the probability of event Ei given event A:
P(Ei|A) = [P(Ei) * P(A|Ei)] / ∑[P(Ej) * P(A|Ej)], for i = 1, 2, …, n
>> Theorem of Total Probability: Given a partition E1, E2, …, En of the sample space and an event A, the theorem of total probability states:
P(A) = P(E1) * P(A|E1) + P(E2) * P(A|E2) + … + P(En) * P(A|En)
>> Random Variables and their Probability Distributions: A random variable is a real-valued function whose domain is a sample space. The probability distribution of a random variable X consists of possible values x1, x2, …, xn and their corresponding probabilities p1, p2, …, pn:
E(X) = μ = ∑(xi * pi)
Var(X) = σ² = ∑((xi - μ)² * pi)
σ = √Var(X)
Free download NCERT Class 12 Maths Chapter 13 Question Answer Probability for CBSE Exam.
NCERT solutions for class 12 maths chapter 13 probability-Exercise: 13.1
Answer:
It is given that and
Question:6 A coin is tossed three times, where
(i)E : head on third toss ,F : heads on first two tosses
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: head on third toss, F: heads on first two tosses
Question:6 A coin is tossed three times, where
(ii)E : at least two heads ,F : at most two heads
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E : at least two heads , F : at most two heads
Question:6 A coin is tossed three times, where
(iii)E : at most two tails ,F : at least one tail
Answer:
The sample space S when a coin is tossed three times is
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
It can be seen that the sample space (S) has 8 elements.
Total number of outcomes
According to question
E: at most two tails, F: at least one tail
Question:7 Two coins are tossed once, where
(i) E : tail appears on one coin, F : one coin shows head
Answer:
E : tail appears on one coin, F : one coin shows head
Total outcomes =4
Question:7 Two coins are tossed once, where
(ii)E : no tail appears,F : no head appears
Answer:
E : no tail appears, F : no head appears
Total outcomes =4
Question:8 A die is thrown three times,
E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Answer:
E : 4 appears on the third toss, F : 6 and 5 appears respectively on first two tosses
Total outcomes
Question:9 Mother, father and son line up at random for a family picture
E : son on one end, F : father in middle
Answer:
E : son on one end, F : father in middle
Total outcomes
Let S be son, M be mother and F be father.
Then we have,
Question:10 A black and a red dice are rolled.
Answer:
A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum greater than and B be a event that the black die resulted in a
Question:10 A black and a red dice are rolled.
Answer:
A black and a red dice are rolled.
Total outcomes
Let the A be event obtaining a sum 8 and B be a event thatthat the red die resulted in a number less than .
Red dice is rolled after black dice.
Question:11 A fair die is rolled. Consider events and Find
Answer:
A fair die is rolled.
Total oucomes
and
Question:11 A fair die is rolled. Consider events and Find
Answer:
A fair die is rolled.
Total oucomes
,
Question:11 A fair die is rolled. Consider events and Find
Answer:
A fair die is rolled.
Total oucomes
and
,
Answer:
Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and B= the youngest is a girl =
Therefore, the required probability is 1/2
Answer:
Assume that each born child is equally likely to be a boy or a girl.
Let first and second girl are denoted by respectively also first and second boy are denoted by
If a family has two children, then total outcomes
Let A= both are girls
and C= at least one is a girl =
Answer:
An instructor has a question bank consisting of 300 easy True / False questions, 200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions.
Total number of questions
Let A = question be easy.
Let B = multiple choice question
easy multiple questions
Therefore, the required probability is 5/9
Answer:
Two dice are thrown.
Total outcomes
Let A be the event ‘the sum of numbers on the dice is 4.
Let B be the event that two numbers appearing on throwing two dice are different.
Therefore, the required probability is 1/15
Answer:
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin.
Total outcomes
Total number of outcomes =20
Let A be a event when coin shows a tail.
Let B be a event that ‘at least one die shows a 3’.
Question:16 In the following Exercise 16 choose the correct answer:
Answer:
It is given that
Hence, is not defined .
Thus, correct option is C.
Question:17 In the following Exercise 17 choose the correct answer:
If and are events such that then
Answer:
It is given that
Hence, option D is correct.
NCERT solutions for class 12 maths chapter 13 probability-Exercise: 13.2
Question:1 If and find if and are independent events.
Answer:
and
Given : and are independent events.
So we have,
Answer:
Two cards are drawn at random and without replacement from a pack of 52 playing cards.
There are 26 black cards in a pack of 52.
Let be the probability that first cards is black.
Then, we have
Let be the probability that second cards is black.
Then, we have
The probability that both the cards are black
Answer:
Total oranges = 15
Good oranges = 12
Bad oranges = 3
Let be the probability that first orange is good.
The, we have
Let be the probability that second orange is good.
Let be the probability that third orange is good.
The probability that a box will be approved for sale
Answer:
A fair coin and an unbiased die are tossed,then total outputs are:
A is the event ‘head appears on the coin’ .
Total outcomes of A are :
B is the event ‘3 on the die’.
Total outcomes of B are :
Also,
Hence, A and B are independent events.
Answer:
Total outcomes .
is the event, ‘the number is even,’
Outcomes of A
is the event, ‘the number is red’.
Outcomes of B
Also,
Thus, both the events A and B are not independent.
Question:6 Let and be events with and Are E and F independent?
Answer:
Given :
and
For events E and F to be independent , we need
Hence, E and F are not indepent events.
Question:7 Given that the events and are such that and Find if they are
Answer:
Given,
Also, A and B are mutually exclusive means .
Question:7 Given that the events and are such that and Find p if they are
Answer:
Given,
Also, A and B are independent events means
. Also
Question:8 Let A and B be independent events with and Find
Answer:
and
Given : A and B be independent events
So, we have
Question:8 Let and be independent events with and Find
Answer:
and
Given : A and B be independent events
So, we have
We have,
Question:8 Let and be independent events with and Find
Answer:
and
Given : A and B be independent events
So, we have
Question:8 Let A and B be independent events with and Find
Answer:
and
Given : A and B be independent events
So, we have
Question:9 If and are two events such that and find
Answer:
If and are two events such that and
use,
Question:10 Events A and B are such that and State whether and are independent ?
Answer:
If and are two events such that and
As we can see
Hence, A and B are not independent.
Question:11 Given two independent events and such that Find
Answer:
Given two independent events and .
Also , we know
Question:11 Given two independent events A and B such that Find
Answer:
Given two independent events and .
Question:12 A die is tossed thrice. Find the probability of getting an odd number at least once.
Answer:
A die is tossed thrice.
Outcomes
Odd numbers
The probability of getting an odd number at first throw
The probability of getting an even number
Probability of getting even number three times
The probability of getting an odd number at least once = 1 - the probability of getting an odd number in none of throw
= 1 - probability of getting even number three times
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
The probability of getting a red ball in first draw
The ball is repleced after drawing first ball.
The probability of getting a red ball in second draw
the probability that both balls are red
(ii) first ball is black and second is red.
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
The probability of getting a black ball in the first draw
The ball is replaced after drawing the first ball.
The probability of getting a red ball in the second draw
the probability that the first ball is black and the second is red
(iii) one of them is black and other is red.
Answer:
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls.
Total balls =18
Black balls = 10
Red balls = 8
Let the first ball is black and the second ball is red.
The probability of getting a black ball in the first draw
The ball is replaced after drawing the first ball.
The probability of getting a red ball in the second draw
the probability that the first ball is black and the second is red
Let the first ball is red and the second ball is black.
The probability of getting a red ball in the first draw
The probability of getting a black ball in the second draw
the probability that the first ball is red and the second is black
Thus,
The probability that one of them is black and the other is red = the probability that the first ball is black and the second is red + the probability that the first ball is red and the second is black
Answer:
and
Since, problem is solved independently by A and B,
probability that the problem is solved
(ii) exactly one of them solves the problem
Answer:
and
,
,
probability that exactly one of them solves the problem
probability that exactly one of them solves the problem
(i) E : ‘the card drawn is a spade’
F : ‘the card drawn is an ace’
Answer:
One card is drawn at random from a well shuffled deck of cards
Total ace = 4
total spades =13
E : ‘the card drawn is a spade
F : ‘the card drawn is an ace’
a card which is spade and ace = 1
Hence, E and F are indepentdent events .
F : ‘the card drawn is a king’
Answer:
One card is drawn at random from a well shuffled deck of cards
Total black card = 26
total king =4
E : ‘the card drawn is black’
F : ‘the card drawn is a king’
a card which is black and king = 2
Hence, E and F are indepentdent events .
(iii) E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’.
Answer:
One card is drawn at random from a well shuffled deck of cards
Total king or queen = 8
total queen or jack = 8
E : ‘the card drawn is a king or queen’
F : ‘the card drawn is a queen or jack’.
a card which is queen = 4
Hence, E and F are not indepentdent events
(a) Find the probability that she reads neither Hindi nor English newspapers
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
the probability that she reads neither Hindi nor English newspapers
(b) If she reads Hindi newspaper, find the probability that she reads English newspaper.
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
The probability that she reads English newspape if she reads Hindi newspaper
(c) If she reads English newspaper, find the probability that she reads Hindi newspaper.
Answer:
H : of the students read Hindi newspaper,
E : read English newspaper and
read both Hindi and English newspapers.
the probability that she reads Hindi newspaper if she reads English newspaper
Question:17 The probability of obtaining an even prime number on each die, when a pair of dice is rolled is
Answer:
when a pair of dice is rolled, total outcomes
Even prime number
The probability of obtaining an even prime number on each die
Option D is correct.
Question:18 Two events A and B will be independent, if
(A) and are mutually exclusive
Answer:
Two events A and B will be independent, if
Or
Option B is correct.
NCERT solutions for class 12 maths chapter 13 probability-Exercise: 13.3
Answer:
Black balls = 5
Red balls = 5
Total balls = 10
CASE 1 Let red ball be drawn in first attempt.
Now two red balls are added in urn .
Now red balls = 7, black balls = 5
Total balls = 12
CASE 2
Let black ball be drawn in first attempt.
Now two black balls are added in urn .
Now red balls = 5, black balls = 7
Total balls = 12
the probability that the second ball is red =
Answer:
BAG 1 : Red balls =4 Black balls=4 Total balls = 8
BAG 2 : Red balls = 2 Black balls = 6 Total balls = 8
B1 : selecting bag 1
B2 : selecting bag 2
Let R be a event of getting red ball
probability that the ball is drawn from the first bag,
given that it is red is .
Using Baye's theorem, we have
Answer:
H : reside in hostel
D : day scholars
A : students who attain grade A
By Bayes theorem :
Answer:
A : Student knows answer.
B : Student guess the answer
C : Answer is correct
By Bayes theorem :
Answer:
A : Person selected is having the disease
B : Person selected is not having the disease.
C :Blood result is positive.
By Bayes theorem :
Answer:
Given : A : chossing a two headed coin
B : chossing a biased coin
C : chossing a unbiased coin
D : event that coin tossed show head.
Biased coin that comes up heads of the time.
Answer:
Let A : scooter drivers = 2000
B : car drivers = 4000
C : truck drivers = 6000
Total drivers = 12000
D : the event that person meets with an accident.
Answer:
A : Items produced by machine A
B : Items produced by machine B
X : Produced item found to be defective.
Hence, the probability that defective item was produced by machine =
.
Answer:
A: the first groups will win
B: the second groups will win
X: Event of introducing a new product.
Probability of introducing a new product if the first group wins :
Probability of introducing a new product if the second group wins :
Hence, the probability that the new product introduced was by the second group :
Answer:
Let, A: Outcome on die is 5 or 6.
B: Outcome on die is 1,2,3,4
X: Event of getting exactly one head.
Probability of getting exactly one head when she tosses a coin three times :
Probability of getting exactly one head when she tosses a coin one time :
Hence, the probability that she threw or with the die =
Answer:
Let A: time consumed by machine A
B: time consumed by machine B
C: time consumed by machine C
Total drivers = 12000
D: Event of producing defective items
Hence, the probability that defective item was produced by =
Answer:
Let A : Event of choosing a diamond card.
B : Event of not choosing a diamond card.
X : The lost card.
If lost card is diamond then 12 diamond cards are left out of 51 cards.
Two diamond cards are drawn out of 12 diamond cards in ways.
Similarly, two cards are drawn out of 51 cards in ways.
Probablity of getting two diamond cards when one diamond is lost :
If lost card is not diamond then 13 diamond cards are left out of 51 cards.
Two diamond cards are drawn out of 13 diamond cards in ways.
Similarly, two cards are drawn out of 51 cards in ways.
Probablity of getting two diamond cards when one diamond is not lost :
The probability of the lost card being a diamond :
Hence, the probability of the lost card being a diamond :
Answer:
Let A : A speaks truth
B : A speaks false
X : Event that head appears.
A coin is tossed , outcomes are head or tail.
Probability of getting head whether A speaks thruth or not is
The probability that actually there was head is
Hence, option A is correct.
Question:14 If and are two events such that and then which of the following is correct?
Answer:
If and then
Also,
We know that
Hence, we can see option C is correct.
NCERT solutions for class 12 maths chapter 13 probability-Exercise: 13.4
Question:1(i) State which the following are not the probability distributions of a random variable. Give reasons for your answer.
Answer:
As we know the sum of probabilities of a probability distribution is 1.
Sum of probabilities
The given table is the probability distributions of a random variable.
Question:1(ii) State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Answer:
As we know probabilities cannot be negative for a probability distribution .
The given table is not a the probability distributions of a random variable.
Question:1(iii) State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Answer:
As we know sum of probabilities of a probability distribution is 1.
Sum of probablities
The given table is not a the probability distributions of a random variable because sum of probabilities is not 1.
Question:1(iv) State which of the following are not the probability distributions of a random variable. Give reasons for your answer.
Answer:
As we know sum of probabilities of a probability distribution is 1.
Sum of probablities
The given table is not a the probability distributions of a random variable because sum of probabilities is not 1.
Answer:
B = black balls
R = red balls
The two balls can be selected as BR,BB,RB,RR.
X = number of black balls.
Hence, possible values of X can be 0, 1 and 2.
Yes, X is a random variable.
Answer:
The difference between the number of heads and the number of tails obtained when a coin is tossed times are :
Thus, possible values of X are 0, 2, 4 and 6.
Question:4(i) Find the probability distribution of
number of heads in two tosses of a coin.
Answer:
When coin is tossed twice then sample space
Let X be number of heads.
X can take values of 0,1,2.
Table is as shown :
X | 0 | 1 | 2 |
P(X) |
|
|
|
Question:4(ii) Find the probability distribution of
number of tails in the simultaneous tosses of three coins.
Answer:
When 3 coins are simultaneous tossed then sample space
Let X be number of tails.
X can be 0,1,2,3
X can take values of 0,1,2.
Table is as shown :
X | 0 | 1 | 2 | 3 |
P(X) |
|
|
|
|
Question:4(iii) Find the probability distribution of
number of heads in four tosses of a coin.
Answer:
When coin is tossed 4 times then sample space
Let X be number of heads.
X can be 0,1,2,3,4
Table is as shown :
X | 0 | 1 | 2 | 3 | 4 |
P(X) |
|
|
|
|
|
Question:5(i) Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as
Answer:
When a die is tossed twice , total outcomes = 36
Number less than or equal to 4 in both toss :
Number less than or equal to 4 in first toss and number more than or equal to 4 in second toss + Number less than or equal to 4 in second toss and number more than or equal to 4 in first toss:
Number less than 4 in both tosses :
Probability distribution is as :
X | 0 | 1 | 2 |
P(X) |
|
|
|
Question:5(ii) Find the probability distribution of the number of successes in two tosses of a die, where a success is defined as
six appears on at least one die .
Answer:
When a die is tossed twice , total outcomes = 36
Six does not appear on any of the die :
Six appear on atleast one die :
Probability distribution is as :
X | 0 | 1 |
P(X) |
|
|
Answer:
Total bulbs = 30
defective bulbs = 6
Non defective bulbs
bulbs is drawn at random with replacement.
Let X : number of defective bulbs
4 Non defective bulbs and 0 defective bulbs :
3 Non defective bulbs and 1 defective bulbs :
2 Non defective bulbs and 2 defective bulbs :
1 Non defective bulbs and 3 defective bulbs :
0 Non defective bulbs and 4 defective bulbs :
the probability distribution of the number of defective bulbs is as :
X | 0 | 1 | 2 | 3 | 4 |
P(X) |
|
|
|
|
|
Answer:
the coin is tossed twice, total outcomes =4
probability of getting a tail be x.
i.e.
Then
and
Let X : number of tails
No tail :
1 tail :
2 tail :
the probability distribution of number of tails are
X | 0 | 1 | 2 |
P(X) |
|
|
|
Question:8(i) A random variable X has the following probability distribution:
Answer:
Sum of probabilities of probability distribution of random variable is 1.
Question:9(a) The random variable X has a probability distribution P(X) of the following form, where k is some number :
Answer:
Sum of probabilities of probability distribution of random variable is 1.
Question:10 Find the mean number of heads in three tosses of a fair coin.
Answer:
Let X be the success of getting head.
When 3 coins are tossed then sample space
X can be 0,1,2,3
The probability distribution is as
X | 0 | 1 | 2 | 3 |
P(X) |
|
|
|
|
mean number of heads :
Question:11 Two dice are thrown simultaneously. If denotes the number of sixes, find the expectation of .
Answer:
denotes the number of sixes, when two dice are thrown simultaneously.
X can be 0,1,2.
Not getting six on dice
Getting six on one time when thrown twice :
Getting six on both dice :
X | 0 | 1 | 2 |
P(X) |
|
|
|
Expectation of X = E(X)
Answer:
Two numbers are selected at random (without replacement) from the first six positive integers in ways.
denote the larger of the two numbers obtained.
X can be 2,3,4,5,6.
X=2, obsevations :
X=3, obsevations :
X=4, obsevations :
X=5, obsevations :
X=6, obsevations :
Probability distribution is as follows:
X | 2 | 3 | 4 | 5 | 6 |
P(X) |
|
|
|
|
|
Answer:
denote the sum of the numbers obtained when two fair dice are rolled.
Total observations = 36
X can be 2,3,4,5,6,7,8,9,10,11,12
Probability distribution is as follows :
X | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
P(X) |
|
|
|
|
|
|
|
|
|
|
|
Standard deviation =
Answer:
Total students = 15
probability of selecting a student :
The information given can be represented as frequency table :
X | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
f | 2 | 1 | 2 | 3 | 1 | 2 | 3 | 1 |
Probability distribution is as :
X | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
P(X) |
|
|
|
|
|
|
|
|
Answer:
Given :
Probability distribution is as :
X | 0 | 1 |
P(X) | 0.3 | 0.7 |
Answer:
X is number representing on die.
Total observations = 6
X | 1 | 2 | 5 |
P(X) |
|
|
|
Option B is correct.
Answer:
X be number od aces obtained.
X can be 0,1,2
There 52 cards and 4 aces, 48 are non-ace cards.
The probability distribution is as :
X | 0 | 1 | 2 |
P(X) |
|
|
|
Option D is correct.
NCERT solutions for class 12 maths chapter 13 probability-Exercise: 13.5
Question:1(i) A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
Answer:
X be the number of success of getting an odd number.
X has a binomial distribution.
Question:1(ii) A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
Answer:
X be a number of success of getting an odd number.
X has a binomial distribution.
Question:1(iii) A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of
Answer:
X be a number of success of getting an odd number.
X has a binomial distribution.
Answer:
A pair of dice is thrown times.X be getting a doublet.
Probability of getting doublet in a throw of pair of dice :
X has a binomial distribution,n=4
Put x = 2
Answer:
There are defective items in a large bulk of items.
X denotes the number of defective items in a sample of 10.
X has a binomial distribution, n=10.
Question:4(i) Five cards are drawn successively with replacement from a well-shuffled deck of cards. What is the probability that
all the five cards are spades?
Answer:
Let X represent a number of spade cards among five drawn cards. Five cards are drawn successively with replacement from a well-shuffled deck of cards.
We have 13 spades.
X has a binomial distribution,n=5.
Put X=5 ,
Question:4(ii) Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
Answer:
Let X represent a number of spade cards among five drawn cards. Five cards are drawn successively with replacement from a well-shuffled deck of cards.
We have 13 spades.
X has a binomial distribution,n=5.
Put X=3 ,
Question:4(iii) Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that
Answer:
Let X represent number of spade cards among five drawn cards. Five cards are drawn successively with replacement from a well-shuffled deck of cards.
We have 13 spades .
X has a binomial distribution,n=5.
Put X=0 ,
Question:5(i) The probability that a bulb produced by a factory will fuse after days of use is . Find the probability that out of such bulbs
none will fuse after days of use.
Answer:
Let X represent number of bulb that will fuse after days of use .Trials =5
X has a binomial distribution,n=5.
Put X=0 ,
Question:5(ii) The probability that a bulb produced by a factory will fuse after days of use is Find the probability that out of such bulbs
not more than one will fuse after days of use.
Answer:
Let X represent a number of the bulb that will fuse after days of use. Trials =5
X has a binomial distribution,n=5.
Put ,
Question:5(iii) The probability that a bulb produced by a factory will fuse after days of use is Find the probability that out of such bulbs
more than one will fuse after days of use.
Answer:
Let X represent number of bulb that will fuse after days of use .Trials =5
X has a binomial distribution,n=5.
Put ,
Question:5(iv) The probability that a bulb produced by a factory will fuse after days of use is . Find the probability that out of such bulbs
at least one will fuse after days of use.
Answer:
Let X represent number of bulb that will fuse after days of use .Trials =5
X has a binomial distribution,n=5.
Put ,
Answer:
Let X denote a number of balls marked with digit 0 among 4 balls drawn.
Balls are drawn with replacement.
X has a binomial distribution,n=4.
Put X = 0,
Answer:
Let X represent the number of correctly answered questions out of 20 questions.
The coin falls heads, he answers 'true'; if it falls tails, he answers 'false'.
X has a binomial distribution,n=20
Question:8 Suppose X has a binomial distribution Show that is the most likely outcome.
(Hint : is the maximum among all of , )
Answer:
X is a random variable whose binomial distribution is
Here , n=6 and .
is maximum if is maximum.
is maximum so for x=3 , is maximum.
Answer:
Let X represent number of correct answers by guessing in set of 5 multiple choice questions.
Probability of getting a correct answer :
X has a binomial distribution,n=5.
Answer:
Let X represent number of winning prizes in 50 lotteries .
X has a binomial distribution,n=50.
Answer:
Let X represent number of winning prizes in 50 lotteries .
X has a binomial distribution,n=50.
Answer:
Let X represent number of winning prizes in 50 lotteries.
X has a binomial distribution,n=50.
Question:11 Find the probability of getting exactly twice in throws of a die.
Answer:
Let X represent number of times getting 5 in 7 throws of a die.
Probability of getting 5 in single throw of die=P
X has a binomial distribution,n=7
Question:12 Find the probability of throwing at most sixes in throws of a single die.
Answer:
Let X represent number of times getting 2 six in 6 throws of a die.
Probability of getting 6 in single throw of die=P
X has a binomial distribution,n=6
Answer:
Let X represent a number of times selecting defective items out of 12 articles.
Probability of getting a defective item =P
X has a binomial distribution,n=12
Answer:
Let X represent a number of defective bulbs out of 5 bulbs.
Probability of getting a defective bulb =P
X has a binomial distribution,n=5
The correct answer is C.
In the following, choose the correct answer:
Answer:
Let X represent number students out of 5 who are swimmers.
Probability of student who are not swimmers =q
X has a binomial distribution,n=5
Option A is correct.
NCERT solutions for class 12 maths chapter 13 probability-Miscellaneous Exercise
Question:1(i) A and B are two events such that Find if
Answer:
A and B are two events such that
Question:2(i) A couple has two children,
Answer:
A couple has two children,
sample space
Let A be both children are males and B is at least one of the children is male.
Question:2(ii) A couple has two children,
Answer:
A couple has two children,
sample space
Let A be both children are females and B be the elder child is a female.
Answer:
We have of men and of women have grey hair.
Percentage of people with grey hairs
The probability that the selected haired person is male :
Answer:
of people are right-handed.
at most of a random sample of people are right-handed.
the probability that more than of a random sample of people are right-handed is given by,
the probability that at most of a random sample of people are right-handed is given by
.
Answer:
Total balls in urn = 25
Balls bearing mark 'X' =10
Balls bearing mark 'Y' =15
balls are drawn with replacement.
Let Z be a random variable that represents a number of balls with Y mark on them in the trial.
Z has a binomial distribution with n=6.
Answer:
Total balls in urn = 25
Balls bearing mark 'X' =10
Balls bearing mark 'Y' =15
balls are drawn with replacementt.
Let Z be random variable that represents number of balls with Y mark on them in trial.
Z has binomail distribution with n=6.
Answer:
Let p and q respectively be probability that the player will clear and knock down the hurdle.
Let X represent random variable that represent number of times the player will knock down the hurdle.
Answer:
Probability of 6 in a throw of die =P
Probability that 2 sixes come in first five throw of die :
Probability that third six comes in sixth throw :
Question:8 If a leap year is selected at random, what is the chance that it will contain 53 tuesdays?
Answer:
In a leap year, there are 366 days.
In 52 weeks, there are 52 Tuesdays.
The probability that a leap year will have 53 Tuesday is equal to the probability that the remaining 2 days are Tuesday.
The remaining 2 days can be :
1. Monday and Tuesday
2. Tuesday and Wednesday
3. Wednesday and Thursday
4. Thursday and Friday
5.friday and Saturday
6.saturday and Sunday
7.sunday and Monday
Total cases = 7.
Favorable cases = 2
Probability of having 53 Tuesday in a leap year = P.
Answer:
Probability of success is twice the probability of failure.
Let probability of failure be X
then Probability of success = 2X
Sum of probabilities is 1.
Let and
Let X be random variable that represent the number of success in six trials.
Answer:
Let the man toss coin n times.
Probability of getting head in first toss = P
The minimum value to satisfy the equation is 4.
The man should toss a coin 4 or more times.
Answer:
In a throw of die,
probability of getting six = P
probability of not getting six = q
There are three cases :
1. Gets six in the first throw, required probability is
The amount he will receive is Re. 1
2.. Does not gets six in the first throw and gets six in the second throw, then the probability
The amount he will receive is - Re.1+ Re.1=0
3. Does not gets six in first 2 throws and gets six in the third throw, then the probability
Amount he will receive is -Re.1 - Re.1+ Re.1= -1
Expected value he can win :
Question:12(i) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
Answer:
'
Let R be the event of drawing red marble.
Let respectively denote the event of selecting box A, B, C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box A is
Question:12(ii) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
Answer:
Let R be event of drawing red marble.
Let respectivly denote event of selecting box A,B,C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box B is
Question:12(iii) Suppose we have four boxes A,B,C and D containing coloured marbles as given below:
Answer:
Let R be event of drawing red marble.
Let respectivly denote event of selecting box A,B,C.
Total marbles = 40
Red marbles =15
Probability of drawing red marble from box C is
Answer:
Let A,E1, E2 respectively denote the event that a person has a heart break, selected person followed the course of yoga and meditation , and the person adopted
the drug prescription.
the probability that the patient followed a course of meditation and yoga is
Answer:
Total number of determinant of second order with each element being 0 or 1 is
The values of determinant is positive in the following cases
Probability is
Answer:
Let E1 and E2 respectively denote the event that red ball is transfered from bag 1 to bag 2 and a black ball is transfered from bag 1 to bag2.
and
Let A be the event that ball drawn is red.
When a red ball is transfered from bag 1 to bag 2.
When a black ball is transfered from bag 1 to bag 2.
Question:17 If A and B are two events such that and then
Choose the correct answer of the following:
Answer:
A and B are two events such that and
Option A is correct.
The conditional probability of an event E, given the occurrence of the event F is given by |
If you are looking for probability class 12 ncert solutions of exercise then they are listed below.
Generally, two questions( 8 marks) are asked from this chapter in 12th board final examination. You can score these 8 marks very easily with the help of probability Class 12 ncert solutions chapter 13.
In the NCERT textbook there are 37 solved examples are given, so you can understand the concept easily. In this chapter 13 12 th class, there is a total of 81 questions in 5 exercises. You should try to solve every question given in chapter 13 class 12 maths on your own.
If you are not able to do, you can take the help of these NCERT solutions for class 12 maths chapter 13 probability. These probability class 12 NCERT questions are solved and explained in a step-by-step manner, so it can be understood very easily.
This chapter 13 12 th class requires lots of practice to understand it better. So, you are advised to solve miscellaneous exercise of probability class 12 ncert solutions.
13.1 Introduction
13.2 Conditional Probability
13.2.1 Properties of conditional probability
13.3 Multiplication Theorem on Probability
13.4 Independent Events
13.5 Bayes' Theorem
13.5.1 Partition of a sample space
3.5.2 Theorem of total probability
13.6 Random Variables and its Probability Distributions
13.6.1 Probability distribution of a random variable
13.6.2 Mean of a random variable
13.6.3 Variance of a random variable
13.7 Bernoulli Trials and Binomial Distribution
13.7.1 Bernoulli trials
13.7.2 Binomial distribution
As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
Comprehensive explanations: The probability ncert class 12 solutions provided in NCERT Solutions for Class 12 Maths Chapter 13 Probability are explained in a comprehensive and step-by-step manner. This helps students to understand the concepts better and makes it easy for them to solve similar problems.
Easy to understand: The probability solutions class 12 are written in simple language, making it easy for students to understand and learn the concepts. The solutions are designed to cater to the needs of students of all learning levels.
Covers all the topics: The class 12 probability solutions cover all the topics in Chapter 13 Probability of Class 12 Maths. This helps students to have a comprehensive understanding of the chapter.
Exercise-wise solutions: The class 12 chapter 13 maths solutions are provided exercise-wise, which helps students to focus on specific problems and concepts that they find difficult.
Examples and illustrations: The ch 13 maths class 12 solutions include examples and illustrations to explain the concepts and solutions better. These examples help students to understand the applications of probability in real-life situations.
Benefits of NCERT solutions
NCERT solutions for Class 12 Maths Chapter 13 are very easy to understand as these are prepared and explained in a detailed manner.
At the end of every chapter, there is an additional exercise called Miscellaneous exercise which is very important for you if you wish to develop a grip on the concepts. In NCERT solutions for class 12 maths chapter 13 probability, you will get solutions for miscellaneous exercise too.
These NCERT solutions for Class 12 Maths Chapter 13 PDF download are prepared with different approaches so it will give you new ways of solving the problems.
NCERT solutions for class 12 maths chapter 13 probability are prepared and explained by the experts who know how best to answer the questions in the board exam. So, it will help you to score good marks in the exam.
Happy Reading !!!
Basic probability, conditional probability, properties of conditional probability, multiplication theorem on probability, independent events, Bayes' theorem, random variables, and its probability distributions, Bernoulli trials, and Binomial distribution are important topics of this chapter.
No, CBSE doesn’t provide NCERT solutions for any class or subject. but there are so many coaching institutions which provide solutions freely. if you are interested then you can download these from careers360 official website.
Students consider integration and application of integration as the most difficult chapters in CBSE class 12 maths but with rigorous practice, you will get conceptual clarity and will be able to have a strong grip on them also.
hello,
Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.
I hope this was helpful!
Good Luck
Hello dear,
If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.
As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.
Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.
Believe in Yourself! You can make anything happen
All the very best.
Hello Student,
I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects and we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.
You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.
All the best.
If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.
Yes, you can take admission in class 12th privately there are many colleges in which you can give 12th privately.
The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.
A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.
Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.
Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.
The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction.
The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions.
How fascinating it is to represent the whole world on just a piece of paper or a sphere. With the help of maps, we are able to represent the real world on a much smaller scale. Individuals who opt for a career as a cartographer are those who make maps. But, cartography is not just limited to maps, it is about a mixture of art, science, and technology. As a cartographer, not only you will create maps but use various geodetic surveys and remote sensing systems to measure, analyse, and create different maps for political, cultural or educational purposes.
Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.
The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.
Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.
An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.
Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.
An expert in plumbing is aware of building regulations and safety standards and works to make sure these standards are upheld. Testing pipes for leakage using air pressure and other gauges, and also the ability to construct new pipe systems by cutting, fitting, measuring and threading pipes are some of the other more involved aspects of plumbing. Individuals in the plumber career path are self-employed or work for a small business employing less than ten people, though some might find working for larger entities or the government more desirable.
Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.
Urban Planning careers revolve around the idea of developing a plan to use the land optimally, without affecting the environment. Urban planning jobs are offered to those candidates who are skilled in making the right use of land to distribute the growing population, to create various communities.
Urban planning careers come with the opportunity to make changes to the existing cities and towns. They identify various community needs and make short and long-term plans accordingly.
Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.
Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.
A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability.
Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.
A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.
Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.
An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.
The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.
The hospital Administrator is in charge of organising and supervising the daily operations of medical services and facilities. This organising includes managing of organisation’s staff and its members in service, budgets, service reports, departmental reporting and taking reminders of patient care and services.
For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.
Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.
Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.
Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.
Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.
A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.
A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.
A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.
In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.
Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.
For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.
In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.
Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.
Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.
Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning).
Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian.
The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack
As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters
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