(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,