Three manufacturing plants, say I, II and III, produce 20, 30 and 50 percent of a company’s output respectively. What is the probability that a randomly-chosen item from the company’s warehouse is defective?
The manager of plant III is very quality conscious and only 1% of the items from that plant are defective. Plants I and II have defective rates of 3% and 5% respectively.
An item is selected at random from the company’s warehouse and found to be defective. What is the probability it was manufactured in plant III?