-->

Probability

Question
CBSEENMA12033635

If A and B are two independent events such that P(A ∪ B) = 0.6 and P(A) = 0.2, find P(B).

Solution

    straight P left parenthesis straight A space union straight B right parenthesis space equals space 0.6 comma space space space straight P left parenthesis straight A right parenthesis space equals space 0.2
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 space space space space space 0.6 space equals space 0.2 space plus space straight P left parenthesis straight B right parenthesis space minus space straight P left parenthesis straight A right parenthesis. space space straight P left parenthesis straight B right parenthesis space space 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 space 0.6 space equals space 0.2 space plus space straight P left parenthesis straight B right parenthesis space minus space left parenthesis 0.2 right parenthesis. space space space straight P left parenthesis straight B right parenthesis
rightwards double arrow space space space space space space space space space 0.4 space equals space left parenthesis 0.8 right parenthesis space space space straight P left parenthesis straight B right parenthesis space space space 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 fraction numerator 0.4 over denominator 0.8 end fraction space equals 1 half space equals 0.5

Some More Questions From Probability Chapter