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 $P\left(A/B\right)$ and $P\left(B/A\right)$.

Answer 1

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

Clearly,$A=\{MFS,FMS,SMFSFM\},B=\{MFS,SFM\}$ and so $A\cap B=\{MFS,SFM\}$

$\therefore P\left(A/B\right)=\frac{P(A\cap B)}{P\left(B\right)}=\frac{2/6}{2/6}=1$
and, $P\left(B/A\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{2/6}{4/6}=\frac{1}{2}$