If $P(A ∩ B)= \frac{1}{3}, P(A ∪ B)=\frac{5}{6}$ and $P(A)=\frac{1}{2}$, then which one of the following is coorect?

A and B are independent events A and B are mutually exclusive events $P(A)= P(B)$ $P(A)< P(B)$

A and B are independent events

We have, $P( A ∪ B) = P(A) + P(B) - P(A ∩ B)$ $⇒ \frac{5}{6}=\frac{1}{2}+P(B)-\frac{1}{3}⇒ P(B)=\frac{2}{3}$ Clearly, $P(A ∩ B) = P(A) P(B)$ So, A and B are independent events.