A company producing electric relays has three manufacturing plants producing 33,42 and 25 percent, respectively, of its product. Suppose that the probabilities that a relay manufactured by these plants is defective are 0.01, 0.005 and 0.03, respectively a. If a relay is selected at random from this company, what is the probability that it is defective? If a relay selected at random is found to be de fective, what is the probability that it was manufactured at the third plant? b. Now compare empirically determined results versus theoretically predicted results for Problem #2. Follow this approach: Write a MATLAB function relay.m to simulate the manufacture of the relays. Your function should accept 6 parameters: the individual probabilities of being manufactured at each plant as well as the probability of being defective for each plant. Your function might return 4 parameters: a flag for each plant to indicate if the part was manufactured at that plant (only one of these will be TRUE) and a flag to indicate if the part manufactured at that plant was defective. Note that the manufacture of the relays is a disjoint event; manufacturing at one plant implies the relay was not manufactured at the other plants. Hence, you should only use a single call to rand to assign the active manufacturing plant. Use another call to rand to determine if the part is de fective. * As in the first problem, the empirically found probabilities should be determined by finding the appropriate average as a ratio of two quantities. Run your relay function many times and compute your empirical result. Neatly report your empirically determined results to the user using formatted output. Again, is good practice to compare your empirical results to the theoretically determined quantities (theoretical results may be hardcoded in this case as well)