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  4. If two events A and B are such that P(AC) = 0.3, P(B) = 0.4 and P(A ∩ Bc) = 0.5, then P[B/(A ∪ Bc)] is equal to

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Q. If two events $A$ and $B$ are such that $P(A^C) = 0.3, P(B) = 0.4$ and $P(A \cap B^c) = 0.5$, then $P[B/(A \cup B^c)]$ is equal to

Probability - Part 2

Solution:

$P[B/(A \cup B^c)] = \frac{P(B \cap (A \cup B^c))}{P(A \cup B^c)}$
$ = \frac{P(A \cap B)}{P(A) + P(B^c) - P(A \cap B^c)}$
$ = \frac{P(A) - P(A \cap B^c)}{P(A) + P(B^c) - P(A \cap B^c)} $
$= \frac{0.7 - 0.5 }{0.8} = \frac{1}{4}$