Q. If $M$ and $N$ are any two events. The probability, that exactly one of them occurs, is
A) $P(M) + P(N) - P(M \cap N)$
B) $P(M) + P(N) + P(M \cap N)$
C) $P(M) + P(N)$
D) $P(M) + P(N) - 2P(M \cap N)$
Explanation
(d)
$\because$ Probability $= P\left( M \cap \overline{N} \right) + P(\overline{M} \cap N)$
$\Rightarrow \ P = P(M) - P(M \cap N) + P(N) - P(M \cap N)$
$\Rightarrow \ P = P(M) + P(N) - 2P(M \cap N)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.