If A and B are events such that $P(A) = 0.4,P(B) = 0.3$ and $P(A \cup B) = 0.5$, then $P\left( {{B^\prime } \cap A} \right)$ equals to

Here, $P(A) = 0.4,P(B) = 0.3$ and $P(A \cup B) = 0.5$

$\Rightarrow$ $P(A \cap B) = 0.4 + 0.3 - 0.5 = 0.2$
$\therefore$ $P\left( {{B^\prime } \cap A} \right) = P(A) - P(A \cap B)$

$= 0.4 - 0.2 = 0.2 = \frac{1}{5}$