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Probability

Question
CBSEENMA12033637
Wired Faculty App

If P(not B) = 0.65, P( A ∪ B) = 0.85 and A, B are independent events, find the value of P(A).

Solution

       P(not B) = 0.65
rightwards double arrow space space space space 1 minus straight P left parenthesis straight B right parenthesis space equals space 0.65 space space space space space space space space rightwards double arrow space space space space straight P left parenthesis straight B right parenthesis space equals space 0.35 comma space space straight P left parenthesis straight A union straight B right parenthesis space equals space 0.85
Now,   straight P left parenthesis straight A union straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A intersection straight B right parenthesis
rightwards double arrow space space space space space straight P left parenthesis straight A union straight B right parenthesis space equals space straight P left parenthesis straight A right parenthesis space plus space straight P left parenthesis straight B right parenthesis minus space straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis space space left square bracket because space straight A comma space straight B space are space independent space events right square bracket rightwards double arrow space space space space space space space space 0.85 space space space space space equals space straight P left parenthesis straight A right parenthesis space plus space 0.35 space minus space straight P left parenthesis straight A right parenthesis thin space left parenthesis 0.35 right parenthesis therefore space space space space space space space space space 0.50 space equals space 0.65 space straight P left parenthesis straight A right parenthesis space space space rightwards double arrow space space straight P left parenthesis straight A right parenthesis space equals space fraction numerator 0.50 over denominator 0.65 end fraction space equals 10 over 13

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