Question

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04. What is the probability that at least one of the bonds defaults?

Answer 1

To find the probability that at least one of the bonds defaults, we can use the formula: P(A or B) = P(A) + P(B) - P(A and B). Substituting the given values, the probability is 0.15 or 15%.

Step-by-step explanation:

To find the probability that at least one of the bonds defaults, we can use the formula:

P(A or B) = P(A) + P(B) - P(A and B)

In this case, we have:

P(AA-rated bond defaults) = 0.06

P(A-rated bond defaults) = 0.13

P(both bonds default) = 0.04

Substituting these values into the formula:

P(at least one bond defaults) = 0.06 + 0.13 - 0.04 = 0.15

Therefore, the probability that at least one of the bonds defaults is 0.15 or 15%.