Suppose that Pmale birth 052 A couple wishes to have exactly

Suppose that P(male birth) =0.52 A couple wishes to have exactly two female children in their family. They will have children until this condition is fulfilled . what is the probability that the family has four children

Solution

According to the condition,

Family has two male and two female children.

Also, last child should be a girl.

Therefore , Among first three children exactly two boys should be there. This ia a binomial probability.

P(X=2) = 3C2 * (0.52)^2 * (1-0.52)^1 = 0.39

And P(Last child is girl) = 0.48

Therefore , probability that the family has four children = 0.39*0.48 = 0.1872 Answer

P(Male birth) = 0.52

P(Female birth)

Therefore probability = (0.52)^2 * (1-0.52)^2 =