You have developed a set of criteria for evaluating distressed credits. Companies that do not receive a passing score are classed as likely to go bankrupt within 12 months. You gathered the following information when validating the criteria:
• Forty percent of the companies to which the test is administered will go bankrupt within 12 months: P(non-survivor) = 0.40.
• Fifty-five percent of the companies to which the test is administered pass it: P(pass test) = 0.55.
• The probability that a company will pass the test given that it will subsequently survive 12 months, is 0.85: P(pass test | survivor) = 0.85.
A. What is P(pass test | non-survivor)?
B. Using Bayes' formula, calculate the probability that a company is a survivor, given that it passes the test; that is, calculate P(survivor | pass test).
C. What is the probability that a company is a non-survivor, given that it fails the test?
D. Is the test effective?