$M$ and $N$ are two events such that $P(M \cap N) = 0$. Which of the following is equal to $P(M|(M \cup N))$?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $\frac{P(M)}{P(M) + P(N)}$ ##
$P(M|(M \cup N)) = \frac{P(M \cap (M \cup N))}{P(M \cup N)}$
Since $M$ is a subset of $M \cup N$, $M \cap (M \cup N) = M$.
$= \frac{P(M)}{P(M) + P(N) - P(M \cap N)}$
Given $P(M \cap N) = 0$:
$= \frac{P(M)}{P(M) + P(N)}$