A couple has two children,

(i) Find the probability that both children are males, if it is known that at least one of the children is male.

(ii) Find the probability that both children are females, if it is known that the elder child is a female.

(i) According to the situation, if the couple has two children then the sample space is:

S = {(b, b), (b, g), (g, b), (g, g)}

Let us assume A denote the event of both children having male and B denote the event of having at least one of the male children

Thus, we have:

Hence,

(ii) Let us now assume C denote the event having both children females and D denote the event of having elder child is female

∴ C = {(g, g)}

And, D = {(g, b), (g, g)}

Hence,