Explanation

(c)
Given, $P(A) = \frac{1}{3},\ P(B) = \frac{1}{3}\ and\ P(C) = \frac{1}{4}$
$\therefore P\left( A^{'} \right) = \frac{2}{3},\ P\left( B^{'} \right) = \frac{2}{3}\ and\ P\left( C^{'} \right) = \frac{3}{4}$
Now, $P\left( A^{'} \cap B^{'} \cap C^{'} \right) = P\left( A^{'} \right)P\left( B^{'} \right)P(C^{'})$
$\lbrack\because A,\ B\ and\ C$ are independent events]
$= \frac{2}{3} \times \frac{2}{3} \times \frac{3}{4} = \frac{1}{3}$