Question

If $P(A\cup B)=\frac{2}{3},P(A\cap B)=\frac{1}{6}$ and $P(A)=\frac{1}{3}$ then

• A. A and B are independent events
• B. A and B are disjoint events
• C. A and B are dependent events
• D. None of these

Answer 1

Answer: (A)

$P(A\cup B)=P(A)+P(B)-P(AB)$
$\Rightarrow \frac{2}{3}=\frac{1}{3}+P(B)-\frac{1}{6}$
$\Rightarrow P(B)=\frac{1}{2}$
Now, $P(AB)=P(A)P(B),A$ and $B$ are independent events.