Question

If $A$ and $B$ are two events such that $P(A\cup B)=\frac{5}{6},P(A\cap B)=\frac{1}{3},P\left(A\right)=\frac{2}{3},$ Then $A$ and $B$ are

• A. dependent events
• B. independent events
• C. mutually exclusive events
• D. mutually exclusive and independent events

Answer 1

The correct option is B independent events

We know, $P(A\cup B)+P(A\cap B)=P\left(A\right)+P\left(B\right)$
$\Rightarrow P\left(B\right)=\frac{5}{6}+\frac{1}{3}-\frac{2}{3}=\frac{1}{2}$
So, $P(A\cap B)=P\left(A\right)P\left(B\right)$
$\therefore A$ and $B$ are independent events.