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.

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 :)

Mgraph · Answer

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