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A person throws two fair dice. He wins Rs. 15 for throwing a doublet

( same numbers on the two dice), wins Rs. 12 when the throw results

in the sum of 9 , and loses Rs. 6 for any other outcome on the throw.

Then the expected gain / loss (in Rs.) of the person is :

• Option 1)

gain

• Option 2)

loss

• Option 3)

loss

• Option 4)

2 gain

Option 2) 1/4 loss

For initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is  then the probability that he is unable to solve less than two problem is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Probability of Sonning a  the problems out of 50 problems =   (not sonning ) =   The probability that he is unable to solve less than two problems is :  (zero correct ) +  (one correct) {using Binominal Probability)  Option 1)           Option 2) Option 3) Option 4)

If the data  is such that the mean of first four of these is , the mean of the remaining six is  and the sum of squares of all of these is  ; then the standard deviation of this data is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Variance   standard deviation                                Option 1)   Option 2)    Option 3)     Option 4)

iIf three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Only two equilateral triangle are possible  and    Option 1) Option 2) Option 3) Option 4)

Let a random variable X have a binomial distribution with mean  and variance . If , then k is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

So, the value of  Option 1) Option 2) Option 3) Option 4)

If both the mean and the standard deviation of 50 observations

are equal to 16 ,  then the mean

of  is :

• Option 1)

400

• Option 2)

380

• Option 3)

525

• Option 4)

480

50 observations    .....................(1) ......................(2) So, mean value of  Option 1) 400 Option 2) 380 Option 3) 525 Option 4) 480

Minimum number of times a fair coin must be tossed so that

the probability of getting at least one head is more than 99% is :

• Option 1)

5

• Option 2)

6

• Option 3)

8

• Option 4)

7

So, probability to get atleast one head =      Minimum value of n will be = 7 So, option (4) is correct.  Option 1) 5 Option 2) 6 Option 3) 8 Option 4) 7

If for some , the frequency distribution of the marks

obtained by 20 students in a test is :

 Marks 2 3 5 7 Frequency

then the mean of the marks is :

• Option 1)

3.2

• Option 2)

3.0

• Option 3)

2.5

• Option 4)

2.8

Given that total students = 20 So,  =>  =>   cannot be -ve  So,  Put  correct option (4) Option 1) 3.2 Option 2) 3.0 Option 3) 2.5 Option 4) 2.8

Assume that each born child is equally likely to be a boy or a girl. If two

families have two children each, then the conditional probability that

all children are girls given that at least two are girls is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

There are 4 children  total number of ways in whcih atleast 2 girls are there Required probabilty =  Option (1) is correct. Option 1) Option 2) Option 3) Option 4)

The mean and the median of the following ten numbers in increasing order      are    respectively , then

is equal to  :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1) Option 2) Option 3) Option 4)

Four persons can hit a target correctly with probabilities  and  respectively. If all hit at the target independently, then the probability that the target would be hit,is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

(target is hit)  (No one hit the target) Option 1) Option 2)   Option 3) Option 4)

If the standard deviation of the numbers    is   where   then  is equal to :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Option 1)                Option 2) Option 3) Option 4)

The minimum number of times one has to toss a fair coin so that the probability of observation at least one head is at least 90% is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Let x fair coin tossed 'n' times the P( at least one head)   ( all tail)   Option 1) Option 2) Option 3) Option 4)

A student scores the following marks in five tests : 45,54,41,57,43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Let score of 6th test be x then,  x=48 correct option (i) Option 1) Option 2) Option 3) Option 4)

The mean and variance of seven observations are , respectively. If  of the observations are then the product of the remaining two observations is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Mean Variance Given Option 1) Option 2) Option 3)   Option 4)

Let and be two non-null events such that . Then, which of the following statements is always correct ?

• Option 1)

• Option 2)

• Option 3)

• Option 4)

and non null events (given) Since Option 1) Option 2) Option 3)   Option 4)

In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs.50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Multiplication Theorem of Probability - If A and B are any two events then    - wherein where      The law of Total Probability - Let S be the sample space and E1, E2, ......En be n mutually exclusive and exhaustive events associated with a random experiment. - wherein where A is any event which occurs with E1, E2, E3......En.   p (success)=   p ( 5 or 6 )  =1/3 Option 1)      Option...

Let S = {1,2,.........,20}. A subset B of S is said to be ''nice'' , if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is ''nice'' is:

• Option 1)

• Option 2)

• Option 3)

• Option 4)

Probability of occurrence of an event - Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as  - wherein Where n repeated experiment and E occurs r times.               Possibilities of numbers that can be removed from  (7), (1,6) , (2,5) , (3,4) , (1,2,4)        Option 1)Option 2)Option 3)Option 4)

A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then   is equal to:

• Option 1)

• Option 2)

4

• Option 3)

• Option 4)

ARITHMETIC Mean - For the values x1, x2, ....xn of the variant x the arithmetic mean is given by  in case of discrete data. Standard Deviation - In case of discrete frequency distribution    P(white ball) =  q=         and    n =  16 mean (X) = np =                           = 12 Standard deviation (X) =  Ans.   Option 1)  Option 2)  4Option 3)  Option 4)

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

• Option 1)

• Option 2)

• Option 3)

• Option 4)

ARITHMETIC Mean - For the values x1, x2, ....xn of the variant x the arithmetic mean is given by  in case of discrete data. -     Variance - In case of discrete data  -    Option 1)Option 2)Option 3)Option 4)
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