Financial analysts have developed models based on financial ratios that predict whether or not a company will go bankrupt within the next year.

In a test of one such model, the model correctly predicted the bankruptcy of 88% of firms that in fact did fail. The model also correctly predicted the non-bankruptcy for 82% of firms that did not fail.

Suppose that the model maintains the same reliability when applied to a new group of 82 firms, of which 7 fail in the year following the time at which the model makes its predictions.

1.Define the event F as firm failure and event B as the outcome of a test for bankruptcy.

2.What is the probability that a firm will fail P(F)?