Bond A and Bond B have the same rating and the same probability of default. It is also estimated that: The probability that both Bond A and Bond B will default during the next year is 5%; and If Bond A defaults next year, there is a 50% probability that Bond B will also default. What is the probability that neither Bond A nor Bond B will default over the next year?
A. 75%
B. 80%
C. 85%
D. 95%Answer：C
Assuming P(A) and P(B) are the probabilities of default on bond A and bond B, respectively.
P(A)=P(B), P(AB)=5%, P(B│A)=50%
Thus, P(A)=P(B)=P(AB)/P(B|A)=50%
P(neither Bond A nor Bond B will default over the next year) = 1- P(A or B) = 1- [P(A)+P(B)-P(AB)]=1-(10%+10%-5%)=85%