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  4. If A and B are two independent events, then the probability of occurrence of atleast one of A and B is given by

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Q. If $A$ and $B$ are two independent events, then the probability of occurrence of atleast one of $A$ and $B$ is given by

Probability - Part 2

Solution:

$P$(atleast one of $A$ and $B$)
$= P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= P(A) + P(B) - P(A) P(B)$ [$\because A$, $B$ are independent]
$= P(A) + P(B) [1 - P(A)] = [1 - P(A')] + P(B) P(A')$
$= 1 - P(A') + P(B) P(A') = 1 - P(A') [1 - P(B)]$
$= 1 - P(A') P(B')$