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).

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Solution

The given probabilities are,

P( E )=0.6, P( F )=0.3 and P( E∩F )=0.2

The probability P( E|F ) is calculated as,

P( E|F )= P( E∩F ) P( F ) = 0.2 0.3 = 2 3

The probability P( F|E ) is calculated as,

P( F|E )= P( E∩F ) P( E ) = 0.2 0.6 = 2 6 = 1 3

Therefore, the value of P( E|F )is 2 3 and the value of P( F|E ) is 1 3 .

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