JK accounting firm has noticed that of the companies it audits, 85% show no inve

Question

JK accounting firm has noticed that of the companies it audits, 85% show no inventory shortages, 10%show inventory shortages and 5% show large inventory shortages. JK firm have advised a new accounting test for which it believes the following probabilities hold:

P(company will pass test/no shortages)=0.90

P(company will pass test/small shortage)=0.50

P(company will pass test/large shortage)=0.20

Required:

1)Determine the probability if a company being studied fails this test has large or small inventory shortage

2)If a company being audited passes this test, what is the probabilty of no inventory shortage?

Explanation / Answer

(a)

(0.10*0.50+0.05*0.80)/(0.85*0.10+0.10*0.50+0.05*0.80)

= 0.514285714

(b)

0.90*0.85/(0.90*0.85+0.5*0.1+0.2*0.05)= 0.92727

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