A factory has two machines, A and B. The probability that a randomly selected bolt from the day’s production is defective is 0.05. The probability that a bolt is produced on machine A and is defective is 0.02.
a. (i) Find the probability that a randomly selected bolt was produced on machine A given that it is defective.
b. (ii) Hence determine the probability that a defective bolt was produced on machine B.
c. (iii) Out of 8,000 bolts produced in a day, how many bolts would you expect to be defective and produced on machine A?