An analyst estimates that the probability of default on a seven-year AA-rated bo

Question

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.46, while that on a seven-year A-rated bond is 0.54. The probability that they will both default is 0.35.

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? (Round your answer to 2 decimal places.) Probability

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

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