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True or False: If A and B are two independent events then P(A and B)=P(A).P(B).

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  • Two events $A$ and $B$ associated with a random experiment are independent if occurance of $A$ does not affect the occurance of $B$.
If $A$ and $B$ are independent events probability of occurance of $A$ and $B$
$p(A\cap B)=p(A)p(B/A)$ by multiplication theorem.
$p(B/A)$ is the probability of occurance of $B$
Given that $A$ has occured
But $p(B/A)=p(B) $ as $A$ and $B$ are independent.
There fore $p(A\cap B) =p(A) p(B)$
The given statement is 'True'.
answered Jun 12, 2013 by poojasapani_1