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Question

Mother, Father and son line up at random for a family picture. Find P(A/B), if A and B are defined as follows:
A = Son on one end
B = Father in the middle

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Solution

The total number of ways in which Mother(M), Father(F) and Son(S) can be lined up at random in one of the following ways:
MFS,MSF,FMS,FSM,SFM,SMF

A=SMF,SFM,MFS,FMS and B=MFS,SFM

Therefore,
AB=MFS,SFM
n(AB)=2 and n(B)=2

Therefore,
Required probability = P(A/B)=n(AB)n(B)=22=1

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