Question

Assume each newborn baby has a probability of approximately 0.470 of being female and 0.530 of being male. For a family with four children, find the probability that the family has two girls and two boys

Answer 1

Let X be a random variable which denotes the number of children which are girls.

According to question n= no. of children =4 and X=2 and p(x)= 0.470 , q(x) = 0.530

Also they are independent of each other i.e If a 1st child is girl it does not effect other child sex, they can be girl or boy .

Also p is constant here. Hence X satisfies all the conditions of Binomial distribution.

So , P( Two girls and two boys ) =P(X=2) =  ⁴C₂ ( 0.470 )² ( 0..530 )²

= ( 4!/2! 2! ) * 0.06205 = 6 * 0.06205

= 0.37230