Using detailed cash-flow information, a financial analyst claims to be able to s

Question

Using detailed cash-flow information, a financial analyst claims to be able to spot companies that are likely candidates for bankruptcy. The analyst is presented with information on the past records of 15 companies and told that, in fact, 5 of these have failed. He selects as candidates for failure 5 companies from the group of 15. In fact, 3 of the 5 companies selected by the analyst were among those that failed. Evaluate the financial analyst’s performance on this test of his ability to detect failed companies.

Explanation / Answer

Suppose the financial analyst picked 5 companies completely randomly out of the given set of 15 companies. Let X be the number of failed companies picked by a financial analyst. Calculate the prabability of picking less than 3 failed companies.

P(X<3)

= P(X=0) + P(X=1) + P(X=2)

= [(5C0 ×10C5)/10C5]   +   [(5C1 ×10C4)/10C5]    +   [(5C2 ×10C3)/10C5]

= [(1 × 252)/3003] + [(5 × 210)/3003] + [(10 × 120)/3003]

= (252/3003) + (1050/3003) + (1200/3003)

= 0.0839 + 0.3497 + 0.3996

= 0.8332

That is, if the financial analyst had picked the companies randomly, there was a high probability of 83.32% of picking less than 3 failed companies. Since he picked 3 failed companies, he did pretty well.

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