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  4. If A and B are two events such that P(A) = (1/3), P(B) = (1/2) and P(A∩ B) = (1/6), then P(A'|B) is

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Q. If A and B are two events such that $P(A) = \frac{1}{3}, \, P(B) = \frac{1}{2}$ and $P(A\cap B) = \frac{1}{6}$, then P(A'|B) is

KCETKCET 2020

Solution:

Given $P(A)=1 / 3, P(B)=1 / 2, P(A \cap B)=1 / 6$
So, $P\left(A' | B\right)=1-P(A | B)$
$= 1 - \frac{P(A \cap B)}{P(B)}$
$=1-1 / 3$
$=2 / 3$