Sponsor Area

Probability

Question
CBSEENMA12033636

If P(not A) = 0.4, P(A ∪ B) = 0.75 and A, B are given to be independent events, find the value of P(B).

Solution
straight P left parenthesis space not space straight A right parenthesis space equals space 0.4 space space space space space space space space space space space space space space rightwards double arrow space space space space space 1 minus space straight P left parenthesis straight A right parenthesis space equals space 0.4
rightwards double arrow space space space space space space space space straight P left parenthesis straight A right parenthesis space equals space 0.6 comma space space space straight P left parenthesis straight A union straight B right parenthesis space equals space 0.75
Now 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 space minus space straight P left parenthesis straight A intersection straight B right parenthesis
therefore 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 space minus space straight P left parenthesis straight A right parenthesis space straight P left parenthesis straight B right parenthesis space space space open square brackets because space straight A comma space straight B space are space independent space events close square brackets
therefore space space space space space space space space 0.75 space equals space 0.6 space plus space straight P left parenthesis straight B right parenthesis space minus space 0.6 space straight P left parenthesis straight B right parenthesis
rightwards double arrow space space space space space space space space space space space 0.15 space equals space 0.4 space straight P thin space left parenthesis straight B right parenthesis space space space space space space space space space space rightwards double arrow space space space space space space space straight P left parenthesis straight B right parenthesis space equals space fraction numerator 0.15 over denominator 0.4 end fraction space equals 3 over 8

Sponsor Area

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