If $P(A) = 0.4$, $P(B) = 0.8$ and $P(B \mid A) = 0.6$, then $P(A \cup B)$ is equal to

$0.96$

The correct answer is Option (4) → $0.96$ ##

Here, $P(A) = 0.4, P(B) = 0.8$ and $P(B \mid A) = 0.6$

$∵P(B \mid A) = \frac{P(B \cap A)}{P(A)}$

$\Rightarrow P(B \cap A) = P(B \mid A) \cdot P(A)$

$= 0.6 \times 0.4 = 0.24$

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

$= 0.4 + 0.8 - 0.24$

$= 1.2 - 0.24 = 0.96$