Answer all questions below. Make sure to show your work whenever appropriate. A foreman for an injection-molding firm admits that, on 35% of his shifts, he forgets to shut off the injection machine on his line. This causes the machine to overheat and increases the chance that a defective molding will be produced during the early morning run from 4% to 8%. Suppose that the plant manager randomly selects a molding from the morning run: a. What are the prior probabilities in this problem? (4 points) b. Write the conditional probabilities based on the new event of interest. (4 points) c. What is the probability that a molding selected is defective? (2 points) d. If the plant manager randomly selects a molding from the morning run and finds it to be defective, what is the probability that the foreman forgot to shut off the machine the previous night? (4 points) e. What is the probability that a molding selected is not defective? (2 points) . If the plant manager randomly selects a molding from the morning run and finds it to be non-defective, what is the probability that the oreman forgot to shut off the machine the previous night? (4 points)