Mother, father and son line up at random for a family picture

If mother (M), father (F), and son (S) line up for the family picture, then the sample space will be

S = {MFS, MSF, FMS, FSM, SMF, SFM}

$\Rightarrow \mathrm{E}=\{\mathrm{MFS}, \mathrm{FMS}, \mathrm{SMF}, \mathrm{SFM}\}$

F = {MFS, SFM}

$\therefore \mathrm{E} \cap \mathrm{F}=\{\mathrm{MFS}, \mathrm{SFM}\}$

$\therefore E \cap F=\{M F S, S F M\}$

$P(E \cap F)=\frac{2}{6}=\frac{1}{3}$

$P(F)=\frac{2}{6}=\frac{1}{3}$

$\therefore P(E \mid F)=\frac{P(E \cap F)}{P(F)}=\frac{\frac{1}{3}}{\frac{1}{3}}=1$