Question

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:
- Twenty percent of the companies to which the test is administered will go bankrupt within 12 months: P(nonsurvivor) = 0.20
- Twenty percent of the companies to which the test is administered pass it: P(pass test) = 0.20
- The probability that a company will pass the test given that it will subsequently survive 12 months is 0.125: P(pass test | survivor) = 0.125

a. What is P(nonsurvivor | fails test)?

b. What is P(pass test | nonsurvivor)?

c. What is P(survivor | pass test)?

Answer 1

(b) Survive, P = 1 – 0.40 = 0.6

P(A) = P(A|B)P(B) + P(A|~B)P(~B)

P(pass test) = P(pass test|survivor)P(survivor) + P(pass test|nonsurvivor)P(nonsurvivor)

0.20 = 0.125 × 0.80 + P(pass test|nonsurvivor) × 0.20

P(pass test|nonsurvivor) = (0.20 – 0.125 × 0.80) / 0.40 = 0.25

(c) P(survivor|pass test) = P(pass test|survivor)*P(survivor)/P(pass test)

= 0.125 × 0.80 / 0.20 = 0.50

(a) P(nonsurvivor|fail test) = P(fail test|nonsurvivor)*P(nonsurvivor)/P(fail test)

[1 – P(pass test|nonsurvivor)] × 0.20 / (1 - 0.20)

= 0.75 × 0.20 / 0.80

=0.1875