An analyst estimates that the probability of default on a seven-year AA rated bo
ID: 2921545 • Letter: A
Question
An analyst estimates that the probability of default on a seven-year AA rated bond is 0.12, while that on a seven-year A rated bond is 0.13. The probability that they will both default is 0.07.
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 0.12, while that on a seven-year A rated bond is 0.13. The probability that they will both default is 0.07.
Explanation / Answer
A: default on a seven-year AA rated bond
B: default on a seven-year A rated bond
It is given that P(A)=0.12, P(B)=0.13 and P(A and B)=0.07
P(A or B)=P(A)+P(B)-P(A and B)=0.12+0.13-0.07=0.18
a) P(atleast one defaults)=1-P(none defaults)=1-P(not (A or B))=1-(1-0.18)=0.18
b) P(not (A or B))=1-0.18 =0.82
c) P(B|A)= P(A and B)/P(B)=0.07/0.13=0.54