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Maths-

General

Easy

Question

If A and B are two independent events, then A and $stack B with ̄ on top$ are

Not independent
Also independent
Mutually exclusive
None of these

The correct answer is: Also independent

Since $A intersection stack B with ̄ on top$ and $A intersection B$ are mutually exclusive events such that $A equals left parenthesis A intersection stack B with ̄ on top right parenthesis union left parenthesis A intersection B right parenthesis$
\ $P left parenthesis A right parenthesis equals P left parenthesis A intersection stack B with ̄ on top right parenthesis plus P left parenthesis A intersection B right parenthesis$
$rightwards double arrow P left parenthesis A intersection stack B with ̄ on top right parenthesis equals P left parenthesis A right parenthesis minus P left parenthesis A intersection B right parenthesis equals P left parenthesis A right parenthesis minus P left parenthesis A right parenthesis P left parenthesis B right parenthesis$
$left parenthesis because A comma B$ are independent)
$rightwards double arrow P left parenthesis A intersection stack B with ̄ on top right parenthesis equals P left parenthesis A right parenthesis left parenthesis 1 minus P left parenthesis B right parenthesis right parenthesis equals P left parenthesis A right parenthesis P left parenthesis stack B with ̄ on top right parenthesis$
$therefore A$ and $stack B with ̄ on top$ are also independent.

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