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Probability

Question
CBSEENMA12033579

Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P(E | F) and P(F | E).

Solution
Here P(E) = 0.6, P(F) = 0.3, P(E ∩ F) = 0.2
Now,           straight P left parenthesis straight E space left enclose space straight F end enclose right parenthesis space equals space fraction numerator straight P left parenthesis straight E space intersection space straight F right parenthesis over denominator straight P left parenthesis straight F right parenthesis end fraction space equals space fraction numerator 0.2 over denominator 0.3 end fraction space equals 2 over 3
and      straight P left parenthesis straight F space left enclose straight E right parenthesis space equals space fraction numerator straight P left parenthesis straight F intersection straight E right parenthesis over denominator straight P left parenthesis straight E right parenthesis end fraction space equals fraction numerator straight P left parenthesis straight E intersection straight F right parenthesis over denominator straight P left parenthesis straight E right parenthesis end fraction equals space fraction numerator 0.2 over denominator 0.6 end fraction equals space 2 over 6 space equals 1 third

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