It is given that the events A and B are such that $straight P left parenthesis straight A right parenthesis space equals space 1 fourth comma space straight P space open parentheses straight A over straight B close parentheses space equals space 1 half space and space straight P space open parentheses straight B over straight A close parentheses space equals space 2 over 3$ then P(B) is

1/6

1/3

2/3

1/2

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Solution

1/3

fraction numerator straight P left parenthesis straight A intersection straight B right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space 1 half comma fraction numerator straight P space left parenthesis straight A intersection straight B right parenthesis over denominator straight P space left parenthesis straight A right parenthesis end fraction space equals space 2 over 3 Hence space fraction numerator straight P left parenthesis straight A right parenthesis over denominator straight P left parenthesis straight B right parenthesis end fraction space equals space 3 over 4 space space left parenthesis But space straight P space left parenthesis straight A right parenthesis space equals space 1 divided by 4 right parenthesis rightwards double arrow space straight P left parenthesis straight B right parenthesis space equals space 1 third

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