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Events E and F are such that P(not E or not F)=0.25.state whether E and F are mutually exclusive.

$\begin{array}{1 1}(A)\;\text{Mutually exclusive}\\(B)\;\text{Not mutually exclusive}\end{array} $

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  • According to Demorgan's law $E'\cup F'=(E \cap F)'$
Given $P(E'\cup F')=P(E \cap F)'=0.25$
$\therefore P(E \cap F)'=1-P(E \cap F)$
$\Rightarrow P(E \cap F)=1-P(E \cap F)'$
$\Rightarrow 1-0.25$
$\Rightarrow 0.75\neq 0$
$\therefore$ E and F are not mutually exclusive.
Hence (B) is the correct answer.
answered Jul 1, 2014 by sreemathi.v

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