Question

Supposed (as is roughly correct) that each child born is equally likely to be a boy or a girl and that sexes of successive children are independent. If we let BG mean that the older child is a boy, and the younger child is a girl, then each of the combinations BB, BG, GB, GG has probability 0.25. Ashley and Brianna each have two children.

a.) You know that at least one of Ashley's children is a boy. What is the conditional probability that she has two boys?

b.) You know that Brianna's older child is a boy. What is the conditional probability that she has two boys?


please help, if you can :)

Answer 1

The formula of the conditional probability

P(X\Y)=P(XY)/P(Y)

a)Y="at least one is a boy"
Y=BB+BG+GB, P(Y)=3/4
X=BB
If X then Y => XY=X P(XY)=P(X)=1/4
P(X\Y)=(1/4)/(3/4)=1/3

b)Y="the older child is a boy"
Y=BB+BG, P(Y)=1/2
X=BB, XY=X, P(XY)=1/4
P(X/Y)=(1/4)/(1/2)=1/2