Having a lot of trouble with Bayes’ formula. Any tips how to understand / approach this concept? Q) 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(nonsurvivor) = 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. 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). I approached it as: P(survivor) = P(survivor | pass test) (pass test) + P(Survivor | not pass test) (not pass test) . Solution approach is: P(survivor | pass test) = [P(pass test | survivor)/P(pass test)]P(survivor) = (0.85/0.55)0.60 = 0.927273 I have no idea what is going on here? Thank You