Items are inspected for flaws by two quality inspectors. If a flaw is present, it will be detected by the first inspector with probability 0.9, and by the second inspector with probability 0.7. Assume the inspectors function independently. Assume that both inspectors inspect every item and that if an item has no flaw, then neither inspector will detect a flaw. a. Assume that the probability that an item has a flaw is 0.10. If an item is passed by the first inspector, what is the probability that it actually has a flaw?

b. Assume that the probability that an item has a flaw is 0.10. If an item is passed by both inspectors, what is the probability that it actually has a flaw?