A factory has three machines M1,M2 and M3 that manufacture identical screws. The proportions of the daily output coming from the machines are 30%,40% and 30% respectively. The probability that a screw produced by M1 is defective is 0.02, by M2 is 0.03 and by M3 is 0.05. Answer the following:
a. (i) Calculate the probability that a randomly selected screw from the day’s total production is defective.
b. (ii) If the factory produces 60000 screws in a day, determine the expected number of defective screws.