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Prove that if E and F are independent ev...

Prove that if E and F are independent events, then so are the events E and F.

Text Solution

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Two events E and F are independent if
P(E∩F)=P(E)*P(F)
Now,`P(E∩F^')=P(E)-P(E∩F)`
=`P(E)-P(E)P(F)`
=`P(E)[1-P(F)]`
=`P(E)P(F^')`
Hence E and F are independent events.
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