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# True or False: If A and B are independent events,then $P(A'\cup B)=1-P(A)(B')$

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## 1 Answer

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Toolbox:
• (1) If two events $A$ and $B$ associated with an experiment are independent
• $p(A\cap B)=p(A)p(B)$
• (2) For any two events $A$ and $B$
• $p(A\cap B)=p(\overline{A'\cap B'})$
• $=1-p(A'\cap B')$
• (3) $p(\bar{A})=1-p(A)$
Since $A$ and $B'$ are independent events.
$p(A\cap B')=p(A)p(B')$
Now consider.
$p(A'\cup B)=p(p\overline{(A')'\cap }B')$
=$p(\overline{A\cap B'})$
=$1-p(A \cap B')$
=$1-p(A)p(B')$
The given statement is True
answered Jun 13, 2013

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