$M$ and $N$ are two events such that $P(M \cap N) = 0$. Which of the following is equal to $P(M|(M \cup N))$?

$\frac{P(M)}{P(M) + P(N)}$

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 $P(M \cap N) = 0$:

$= \frac{P(M)}{P(M) + P(N)}$