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Question

Assuming that for a husband wife couple the chances of their child being a boy or a girl are the same, the probability of their two children being a boy and a girl is


A

14

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B

1

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C

12

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D

18

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Solution

The correct option is C

12


Explanation for the correct answer:

Step 1: According to the question.

Let p be the probability of being boy or girl, p=12

Let q be the probability of failure,

q=1-p=1-12=12

Let n be the number of children, n=2

Let x be the number of boys, x=1

Step 2: Applying Binomial distribution formula.

The formula of binomial distribution is

P(x)=nCxpxqn-x

On substituting the above values,

P(boyandgirl)=2C1121122-1=21212...[2C1=2]=12

Thus using binomial distribution, the probability of their two children being a boy and a girl is 12

Hence, option (C) 12 is the correct answer.


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