Q. If $P(A) = 1/3,P(B) = 1/2$ and $P(A \cup B) = 5/6$, then events $A\ and\ B$ are
A) Mutually exclusive
B) Independent as well as mutually exhaustive
C) Independent
D) Dependent only on $A$
Explanation
(a)
We know, $P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$\frac{5}{6} = \frac{1}{3} + \frac{1}{2} - \ P(A \cap B)$
$\Rightarrow \frac{5}{6} = \frac{5}{6} - P(A \cap B)$
$\Rightarrow \ P(A \cap B) = 0$
$\therefore$ Events $A\ and\ B$ are mutually exclusive.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.