Question

Mother, Father and son line up at random for a family picture. Find $P\left(A/B\right)$, if A and B are defined as follows:

A = Son on one end

B = Father in the middle

Answer 1

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,

$A\cap B=MFS,SFM$

$n(A\cap B)=2$ and $n\left(B\right)=2$

Therefore,

Required probability = $P\left(A/B\right)=\frac{n(A\cap B)}{n\left(B\right)}=\frac{2}{2}=1$