An analyst estimates that the probability of default on a seven-year AA-rated bo
ID: 3024406 • Letter: A
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. a. What is the probability that at least one of the bonds defaults? (Round your answer to 2 decimal places.) Probability b. What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults? (Round your answer to 2 decimal places.) Probability c. Given that the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults?
Explanation / Answer
P( default on a seven-year AA-rated bond ) = 0.06
P( seven-year AA-rated bond ) = 0.13
P( probability that they will both default ) = 0.04
a. What is the probability that at least one of the bonds defaults?
Answer = 0.06 + 0.13 - 0.04 = 0.15
b. 2. What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults?
Answer = 1-P(at least one of the bonds defaults) = 1 - 0.15 = 0.85
c. 3. Given that the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults?
Answer = 0.04/0.06 = 0.6667