Question

Mother, father and son line up at random for a family photo. If A and B are two events given by
A = Son on one end, B = Father in the middle, find P(B / A).

Answer 1

If the mother (M), father (F), and son (S) line up for the family picture, then the sample space will be 
A →  Son on one end.
B  → Father in the middle
Son (s) , Father (F), Mother (M)
Total possible cases.
S = {MFS, MSF, FMS, FSM, SMF, SFM}

A= {MFS, FMS, SMF, SFM} 

B = {MFS, SFM}

∴ A ∩ B = {MFS, SFM}

`P(A) = 4/6 = 2/3                    P (A  cap B )  = 2/6 = 1/3`

` P(B) = 2/6 = 1/3`

`P(B/A) = (P(A cap B))/(P(A)) = (1/3)/(2/3) = 1/2`

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