Given that the events A and B are such that P(A) = Find p if they are mutually exclusive. - Wired Faculty

Question

Given that the events A and B are such that P(A) = $1 half comma$ $straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5 space and space straight P left parenthesis straight B right parenthesis space equals space straight p.$ Find p if they are mutually exclusive.

Solution

straight P left parenthesis straight A right parenthesis space equals space 1 half comma space space straight P left parenthesis straight B right parenthesis space equals space straight p comma space space space space straight P left parenthesis straight A union straight B right parenthesis space equals space 3 over 5

Since A and B are mutually exclusive events

therefore space space space space space straight P left parenthesis straight A intersection straight B right parenthesis space equals space 0

...(1)
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

therefore space space space space space space space space space space space 3 over 5 space equals 1 half plus straight p minus 0 space space space space space space space space space space space space space space space space open square brackets because space of space left parenthesis 1 right parenthesis close square brackets rightwards double arrow space space space space space space space space space space space space space space space straight p space equals space 3 over 5 minus 1 half space equals space fraction numerator 6 minus 5 over denominator 10 end fraction space equals 1 over 10

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