Suppose a factory has three machines (I, II, and III) that produce identical items as follows:

I: 500 items per day; 1% defective

II: 200 items per day; 5% defective

III: 300 items per day; 3% defective

Suppose one item is selected at random and tested. Find the probability that item

(a) Is defective.

(b) Came from machine II given that it is defective.