The probability of a firm defaulting each year, given that it has not defaulted in prior years is 10%. What is the probability that it will have defaulted at some time in the first 10 years? Approximately:
A) 50%
B) 65%
C) 80%
D) 100%

Question

Quizplus · Accepted Answer

The probability that a firm does not default in a year is 90%. Therefore, the probability that it does not default in 10 years is (0.9)^10 = 0.3487. The complement of this is the probability that it will have defaulted at some time in the first 10 years, which is 1 - 0.3487 = 0.6513 or approximately 65%. Therefore, the best choice is B.

The Probability of a Firm Defaulting Each Year, Given That