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#### A bag contains slips numbered from 1 to 100. If Fatima chooses a slip at random from the bag, it will either be an odd number or an even number. Since this situation has only two possible outcomes, so, the probability of each is $\frac{1}{2}$ . Justify.

Solution.         Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Total slips = 100
Slips with even number = 50
Probability = $\frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}$
Probability of slip with even number = $\frac{50}{100}= \frac{1}{2}$
Slips with odd number = 50
Probability of slip with odd number = $\frac{50}{100}= \frac{1}{2}$
Hence the probability of each is $\frac{1}{2}$ .

#### If I toss a coin 3 times and get head each time, should I expect a tail to have a higher chance in the 4th toss? Give reason in support of your answer.

Solution.   Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
No, because we get head or tail after tossing a coin that is the probability of both outcomes is $\frac{1}{2}$ .
Hence tail is not have higher chance than head.
Both are have equal chance.

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#### Sushma tosses a coin 3 times and gets tail each time. Do you think that the outcome of next toss will be a tail? Give reasons.

Solution.         Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

No, because when we toss a coin we can get either tail or head and the probability of each is $\frac{1}{2}$.
So, it is not necessary that she gets tail at fourth toss. She can get head also.

#### If you toss a coin 6 times and it comes down heads on each occasion. Can you say that the probability of getting a head is 1? Give reasons.

Solution.    Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
The probability of getting a head is 1, means that we never get tail. But this is not true because we have both head and tail in a coin. Hence probability of getting head is 1 is false.

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#### I toss three coins together. The possible outcomes are no heads, 1 head, 2 heads and 3 heads. So, I say that probability of no heads is $\frac{1}{4}$ . What is wrong with thisconclusion?

Answer.    [$\frac{1}{8}$ ]

Solution.    Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Total cases in tossing three coins = 8(HHH, HHT, HTH, THH, TTT, TTH, THT, HTT)
Number of case with no head = TTT
Probability = $\frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}$
Probability of no head  =$\frac{1}{8}$
The conclusion that probability of no head is $\frac{1}{4}$ is wrong because as we calculate it above, it comes out $\frac{1}{8}$ . Hence the probability of no head is $\frac{1}{8}$

#### A student says that if you throw a die, it will show up 1 or not 1. Therefore, the probability of getting 1 and the probability of getting ‘not 1’ each is equal to $\frac{1}{2}$ . Isthis correct? Give reasons.

Solution.  Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Here total cases = 6
Number of favourable cases in getting 1 = 1
Probability = $\frac{Number\, of\, favourable\ cases, }{Total\, number\, of\, cases}$
Probability of getting $1= \frac{1}{6}$
Number of favourable cases 'not 1' = 5      (2, 3, 4, 5, 6)
Probability of not 1 = $\frac{5}{6}$
Hence they are not equal to $\frac{1}{2}$

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#### When we toss a coin, there are two possible outcomes - Head or Tail. Therefore, the probability of each outcome is $\frac{1}{2}$ . Justify your answer.

Solution.  Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Total cases when we toss a coin = 2(H, T)
Probability = $\frac{Number\, of\, favourable\ cases, }{Total\, number\, of\, cases}$
Probability of head = $\frac{1}{2}$
Probability of tail = $\frac{1}{2}$
Hence the probability of each outcome is $\frac{1}{2}$ .

#### Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number 36? Why

Solution.    Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
As apoorv throws two dice total cases = 36
Product is 36 when he get = (6, 6)
Number of favourable cases = 1
Probability = $\frac{Number\, of\, favourable\ cases }{Total\, number\, of\, cases}$
Probability that Apoorv get 36 = $\frac{1}{36}$
Peehu throws are die total cases = 6
Square of 6 is 36
Hence case = 1
Probability that Peehu get 36 = $\frac{1}{6}$
Hence Peehu has better cases to get 36.

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#### A game consists of spinning an arrow which comes to rest pointing at one of the regions (1, 2 or 3) (Fig.). Are the outcomes 1, 2 and 3 equally likely to occur? Give reasons

Solution.     Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Here 3 contain 50% of the region and 1, 2, contain 25%, 15% of the region.

$Probability= \frac{Number\, of\, favorable\ cases }{Total\, number\, of\, cases}$
$Probability\, of\, 3= \frac{50}{100}= \frac{1}{2}$
$Probability\, of\, 1= \frac{25}{100}= \frac{1}{4}$
$probability\, of\, 2= \frac{25}{100}= \frac{1}{4}$
All probabilities are not equal. So the given statement is false.

#### In a family having three children, there may be no girl, one girl, two girls or three girls. So, the probability of each is  $\frac{1}{4}$ . Is this correct? Justify your answer.

Solution.    Probability: probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Total children = 3
Cases – GGG, GGB, GBG, BGG, BBB, BBG, BGB, GBB were G is girl and B is boy.
Probability = $\frac{Number\, of\, favorable\ cases, }{Total\, number\, of\, cases}$
Probability of 0 girl = $\frac{1}{8}$
Probability of 1 girl = $\frac{3}{8}$
Probability of 2 girl = $\frac{3}{8}$
Probability of 3 girl = $\frac{1}{8}$
Here they are not equal to $\frac{1}{4}$