Probability — Class 12 Maths Solution

.: Let $m,f$ and $S$ denote respectively the mother,

the father and the son, then sample space $S$ is

$S = \{ mfs,{\rm{ }}msf,{\rm{ }}fms,{\rm{ }}fsm,{\rm{ }}smf,{\rm{ }}sfm{\rm{ }}\}$

Let $E:$ 'son on one end' and $F:$ father in the middle',

i.e.a. $E = \{ mfs,{\rm{ }}fms,{\rm{ }}sfm,{\rm{ }}smf{\rm{ }}\}$ and $F = \{ sfm,mfs\}$

$\Rightarrow E \cap F = \{ mfs,sfm\}$
$P(E) = \cfrac{4}{6} = \cfrac{2}{3},P(F) = \cfrac{2}{6} = \cfrac{1}{3},P(E \cap F) = \cfrac{2}{6} = \cfrac{1}{3}$

$\therefore$ $P(E|F) = \cfrac{{P(E \cap F)}}{{P(F)}} = \cfrac{{1/3}}{{1/3}} = 1$