Explanation

(c)
Given, $P(X) = 60\% = \frac{3}{5}$,
$P(Y) = 50\% = \frac{1}{2}$
$\Rightarrow \ P\left( X^{'} \right) = 1 - \frac{3}{5} = \frac{2}{5},$
$P\left( Y^{'} \right) = 1 - \frac{1}{2} = \frac{1}{2}$
$\lbrack\because$ If both speak truth or both speak false narrating the same incident, then thry will not contradict each other].
$\therefore$ Required probability that they contradict each other narrating the same incident$= 1 - \lbrack P(X) \times P\left( Y^{'} \right) + P\left( X^{'} \right) \times P(Y)\rbrack$
$= 1 - \left\lbrack \frac{3}{5} \times \frac{1}{2} + \frac{2}{5} \times \frac{1}{2} \right\rbrack$
$= 1 - \left\lbrack \frac{3}{10} + \frac{2}{10} \right\rbrack = \frac{1}{2}$