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?
Answer & explanation
Correct answer: option 1
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.