1. An accounting firm noticed that of the companies it audits, 85% show no inventory shortages, 10% show small inventory shortages, and 5% show large inventory shortages. The firm has devised a new accounting test for which it believes the following probabilities hold: P(company will pass test | no shortage) = .90 P(company will pass test | small shortage) = .50 P(company will pass test | large shortage) = .20 a. If a company being audited fails this test, what is the probability of a large or small inventory shortage? b. If a company being audited passes this test, what is the probability of no inventory shortage?

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