Machine A produces 3% defectives, machine B produces 5% defectives, and machine C produces 10% defectives. Of the total output from these machines, 60% of the items are from machine A, 30% from B, and 10% from C. One item is selected at random from a day's production.
a. What is the prior probability that the item came from machine C?
b. If inspection finds the item to be defective, what is the revised probability that the item came from machine C?