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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|G) and P (G|E)
Solution
E = {1, 3, 5}, G = {2, 3, 4, 5}, E ∩ G = {3, 5}
P(E) = `3/6`, P(G) = `4/6`, P(E ∩ G) = `2/6`
P(E|G) = `(P(E ∩ G))/(P(G))`
`= (2/6)/(4/6)`
`= 2/4 i.e., 1/2`
P(G|E) = `(P(E ∩ G))/(P(E))`
`= (2/6)/(3/6)`
`= 2/3`
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