An Accounting Firm Has Noticed That of the Companies It

question 16

Short Answer

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?