Evaluate the financial analyst’s performance on this test of his ability to detect failed companies 

1.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. The selected as candidates for failure 5 companies from the group of 15. In fact, 3 of 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 .

2. A team of 5 analysts is about to examine the earnings prospects of 20 corporations. These analysts are not equally competent. In fact, one of them is a star, having an excellent record of anticipating changing trends.Ideally, management would like to allocate the 4 corporations whose earnings will deviate most from past trends to this analyst. However, lacking this information, management allocates corporations to analysts randomly. What is the probability that at least 2 of the 4 corporations whose earnings will deviate most from past trends are allocated to the star analyst?