Let ‘A’, ‘B’ and ‘C’ be three independent events with P(A) = $\frac{1}{3}$, P(B) = $\frac{1}{2}$ and P(C) = $\frac{1}{4}$. The probability of exactly 2 of these events occurring, is equal to

$\frac{1}{4}$

Probability of exactly 2 of the three events happening

$=P(A \cap B)+P(A \cap C)+P(B \cap C)-3 P(A \cap B \cap C)$

$=\frac{1}{3} . \frac{1}{2}+\frac{1}{3} . \frac{1}{4}+\frac{1}{2} . \frac{1}{4}-3 . \frac{1}{3} . \frac{1}{2} . \frac{1}{4}$

$= \frac{1}{4}$