# Two events A and B will be independent, if which of the following is true?

$\begin{array} ((A) A\: and \: B \: are\: mutually\: exclusive & (B) P(A′B′) = [1 – P(A)] [1 – P(B)] \\ (C) P(A) = P(B) \quad & (D) P(A) + P(B) = 1 \end{array}$

## 1 Answer

Toolbox:
• Two events $A$ and $B$ associated with a random experiment are independent if $P(A\cap B)=P(A) P(B)$
• Also If $A$ and $B$ are independent then $A'$ and $B'$ are independent $P(A')=1-P(A)$
Since $A$ and $B$ are independent $A'$ and $B'$ are independent, By definition of independence of events:
$P(A'\cap B')=P(A')P(B')$ =$[1-P(A)][1-P(B)]$
answered Jun 14, 2013
edited Jun 18, 2013

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