Let m, f and s denote respectively the mother, father and the son,
then sample space S is S = {mfs, msf, fms, fsm, smf, sfm},
E : ‘son on one end’ and F : ‘father in the middle’,
i.e., E = {mfs, fms, sfm, smf} and F = {sfm, mfs} ⇒ E ∩ F = {mfs, sfm}
P(E)=

4

6

=

2

3

,P(F)=

2

6

=

1

3

, P(E∩F)=

2

6

=

1

3

∴P(E|F)=

P(E∩F)

P(F)

=

1 3

1 3

=1