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)

Answer 1

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`