Given, a couple has two children.

1. Let A denotes both children are male i.e. {MM}

and B denotes at least one child is male i.e. {MF, FM, MM}

Now, A ∩ B = {MM}

P(A) = (1/2)*(1/2) = 1/4

P(B) = 1/4 + 1/4 + 1/4 = 3/4

So, P(A ∩ B) = 1/4

Now, P(A/B) = P(A ∩ B)/P(B)

=> P(A/B) = (1/4)/(3/4)

=> P(A/B) = 1/3

2. Let A denotes both children are females i.e. {FF}

Now, P(A) = (1/2)*(1/2) = 1/4

and B denotes elder children is a female i.e. {FF, FM}

P(B) = 1/4 + 1/4 = 1/2

Now, P(A ∩ B) = 1/4

Now, P(Both the children are female if elder child is female)

      P(A/B) = P(A ∩ B)/P(B)

=> P(A/B) = (1/4)/(1/2)

=> P(A/B) = 1/2