Question

Determine P(E|F).

Mother, father and son line up at random for a family picture

E: son on one end, F: father in middle

Answer 1

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

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 cap F) = 2/6 = 1/3`

∴ `P (E|F) = (P (E cap F))/(P (F))`

`= (1/3)/(1/3) = 1`