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Question
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|F) and P (F|E)
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Solution
E = {1, 3, 5}, F = {2, 3}, E ∩ F = {3}
P(E) = `3/6`, P(F) = `2/6`, P(E ∩ F) = `1/6`
P(E | F) = `(P(E ∩ F))/(P(F))`
`= (1/6)/(2/6)`
`= 1/2`
P(F | E) = `(P(E ∩ F))/(P(E))`
`= (1/6)/(3/6)`
`= 1/3`
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