Probability

Question

What is conditional probability that a family with 2 children has 2 boys,  given they have atleast 1 boy?

 

Why do we take total cases as 4 { GB, BB, BG, GG}?  Shouldn't we consider GB AND BG same only.

Answer 1

One way:

Reduce the sample space.As here given that, at least one is a boy. So, sample space is {BB,BG,GB}

and our favourable case is BB, so probabiliy is 1/3.

Another way:

Required Probability=Probability of 2 boys/ Probability of at least one boy=(1/4)/(3/4)=1/3