If $A$ and $B$ are events such that $P(A) = 0.4$, $P(B) = 0.3$ and $P(A \cup B) = 0.5$, then $P(B' \cap A)$ is equal to

$\frac{1}{5}$

The correct answer is Option (4) → $\frac{1}{5}$ ##

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

$∵P(A \cup B) = P(A) + P(B) - P(A \cap B)$

$\Rightarrow P(A \cap B) = 0.4 + 0.3 - 0.5 = 0.2$

$∵P(B' \cap A) = P(A) - P(A \cap B) = 0.4 - 0.2 = 0.2 = \frac{1}{5}$