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:\ company will pass test

|

| no shortage

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