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 0.06, 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.) 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 2decimal places.) 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.)

Explanation / Answer

a) P(At least one will default) = 0.06 + 0.13 - 0.04 = 0.15

b) P(Neither bond will default) = 1 - P(Atleast 1 will default) = 1 - 0.15 = 0.85

c) P(A - rated bond defaults | AA - rated bond defaults)

= P(Both default) / P(AA rated bond default)

= 0.04/0.06

= 0.67

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