A couple has two children. Find the probability that 

(i) Both the children are boys, if it is known that the older child is a boy.

(ii) Both the children are girls, if it is known that the older child is girl.

(iii) Both the children are boys, if it is known that at least one of the children is a boy.

Let B_i and G_i (i = 1, 2) stand for the event that i^th child be a boy and a girl respectively. Then, the sample space associated to the random experiment is      

A = {B₁B₂, B₁G₂, G₁, B₂, G₁G₂)

(i) Consider the following events: 

A = Both the children are boys = {B₁B₂}         

B = the older child is a boy ={B₁B₂, B₁G₂} 

∴ A∩B = {B₁B₂}. n (A∩B) = 1 and n(B) = 2