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)

Answer 1

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`