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Question

A family has 5 children. The probability of having a girl is 12. What is the probability of having exactly 3 girls and 2 boys?


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Solution

Finding the required probability:

Let X denote the number of girls in n=5, where each has a probability p=0.5 ,

We can solve it by using the binomial coefficients,

X~(Binomial)(n=5,p=0.5)

The probability of x number of girls is given by the formula:

P(X=x)=Cxnpx(1-p)n-x

Substituting P(X=3),n=5,p=0.5

P(X=3)=C350.53(1-0.5)5-3=10×0.53×0.52=0.313

Therefore, the probability of having exactly 3 girls and 2 boys is 0.313.


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