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 0.53, while that on a seven-year A-rated bond is 0.47. The probability that they will both default is 0.39.

What is the probability that at least one of the bonds defaults? (Round your answer to 2 decimal places.)

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.)

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.)

An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.53, while that on a seven-year A-rated bond is 0.47. The probability that they will both default is 0.39.

Explanation / Answer

given,

probability of default on a seven-year AA-rated bond =P(AA)= 0.53,

while that on a seven-year A-rated bond = P(A) = 0.47

The probability that they will both default = P(A & AA) = 0.39

a) The probability that at least one of the bonds defaults = P(A or AA)

= P(AA) + P(A) - P(A & AA)

= 0.53+ 0.47-0.39 = 0.61

b) The probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults =

1 - the probability that they will both default = 1 - P(A & AA) = 1 - 0.39 = 0.61

c) The probability that the seven-year A-rated bond also defaults, given that the seven-year AA-rated bond defaults = P(A|AA) = P(A & AA) / P(AA) = 0.39/0.53 = 0.74

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