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 of the firm not defaulting in any given year is 90% (or 0.9). To find the probability of it not defaulting over 10 years, we raise this probability to the power of 10: $0.9^{10} \approx 0.3487$. This means there's approximately a 34.87% chance it won't default over 10 years. Subtracting this from 100% gives us the probability that it will default at some point in the first 10 years, which is approximately 65.13%. Therefore, the closest answer is 65%.

The Probability of a Firm Defaulting Each Year,given That It