Let A1, be the event that the items are produced by Machine - I, A, be the event that the items are produced by Machine - II.
Given P(A1) = 60/100 = 3/5
P(A2) = 40/100 = 2/5
P(B | A1) = 2/100 = 1/50
P(B | A2) = 4/100 = 1/25.
We have to find total probability of event B. Since, A1 and A are mutually exhaustive events.
P(B) = P(A1) P(B | A1) + P(A2) P(B | A2)
= 3/5 x 1/50 + 2/5 x 1/25
= 1/125 (3/2 + 2)
= 1/125 x 7/2 = 7/250 = 28/1000 = 0.028
⇒ P(B) = 0.028
∴ The probability that item is defective is 0.028.