It is assumed that when children are born they are equally likely to be boys or girls.What is the probability that a family of four children contains (a) three boys and one girl (b) two boys and two girls

Answer 1

both are binomial distribution problems

prob(boy) = 1/2
prob(girl)

a) in 4 children, we want 3 boys and 1 girl
= C(4,3)(1/2)^3 (1/2)^1
= 4(1/16) = 1/4

b)2 boys, 2 girls
= C(4,2)(1/2)^2 (1/2)^2
= 6(1/16) = 3/8