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

Explanation

The sample space S is given by
`S={MFS,MSF,FSM,FMS,SMF,SFM}`

Clearly,
`A={MFS,FMS,SMF,SFM},B={MFS,SFM}`

and so `AnnB={MFS,SFM}`


`∴ P(A/B)=(P(AnnB)​)/(P(B))=(2/6)/(2/6)​=1`



and, `P(B/A)=(P(A∩B)​)/(P(A))=(2/6)/(4/6)​=1/2`​