If $P(A)=\frac{2}{3}, P(B)=\frac{1}{2}$ and $P(A ∪ B)=\frac{5}{6}$, then events A and B are

independent 

We have, 

$P(A) =\frac{2}{3}, P(B)=\frac{1}{2}$ and $P(A ∪ B)=\frac{5}{6}$

$∴ P(A ∪ B)= P(A) + P(B) - P(A ∪ B)$

$⇒P(A ∪ B) =\frac{2}{3}+\frac{1}{2}-\frac{5}{6}=\frac{1}{3}$

Clearly, P(AB) = P(A)P(B)

Hence, A and B are independent events.

Since independent events are never mutually exclusive.

So, option (c) is correct.