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  4. If P(A ∪ B) = (2/3), P(A ∩ B) = (1/6) and P(A) = (1/3) then

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

BITSATBITSAT 2010

Solution:

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