Let’s consider:
E1 = The event that the item is manufactured on machine A
E2 = The event that the item is manufactured on machine B
E3 = The event that the item is manufactured on machine C
Let H be the event that the selected item is defective.
Thus, by using Baye’s theorem we have
P(E1) = 50/100, P(E2) = 30/100, P(E3) = 20/100
P(H/E1) = 2/100, P(H/E2) = 2/100 and P(H/E3) = 3/100
Therefore, the required probability is 5/11.