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Show small inventory shortages

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An accounting firm has 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? 

Reference no: EM1374692

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