Q5. Use the Total probability and Bayes' Theorem to solve the following question: Three manufacturing plants, say A, B and C, produce 12, 36 and 52 percent of a company's output respectively. The manager of plant C is very quality conscious and only 3% of the items from that plant are defective. Plants A and B have defective rates of 5% and 4% respectively. (Note: Write the formula and/or notation you are using before putting the numbers in. Show your work) a) What is the probability that a randomly chosen item from the company's warehouse is defective? | b) If a randomly chosen item from the company's warehouse is defective what is the probability that it will be produced in Plant B? c) If a randomly chosen item from the company's warehouse is defective what is the probability that it will be produced in Plant C? d) If a randomly chosen item from the company's warehouse is defective what is the probability that it will be produced in Plant A?