Sample space is S = { ff, fm, mf, mm}
where f = female, m = male
(i) Let A = both are male i.e. {mm} ⇒P(A)=

1

4

B = atleast one is a male i.e. {mm, fm, mf } ⇒P(B)=

3

4

A ∩ B = {mm} ⇒P(A∩B)=

1

4

∴ Required probability =P(A|B)=

P(A∩B)

P(B)

=

1∕4

3∕4

=

1

3

(ii) Let A = both are female i.e. { f f } ⇒P(A)=

1

4

B = the elder is a female i.e. { ff, fm} ⇒P(B)=

2

4

A ∩ B = { f f } ⇒P(A∩B)=

1

4

∴ Required probability =P(A|B)=

P(A∩B)

P(B)

=

1∕4

2∕4

=

1

2