Question

Parents have always wondered about the sex of a child before it is born. Suppose that the probability of having a male child was 0.5, and that the sex of one child is independent of the sex of other children. What is the probability of having more than 2 girls out of 10 children? Round your answer to four decimal places.

Answer 1

We have the probability of having a male child was 0.5

So probability of having female child is 1-0.5=0.5

therefore p=0.5

Consider for 10 children

Hence n=10

The sex of one child is independent of the sex of other children.

Therefore this is binomial distribution.

X~B(n=10, p=0.5)

The probability of having more than 2 girls out of 10 children is,

Hence The probability of having more than 2 girls out of 10 children is 0.9453