题目
Bonds rated B have a 25% chance of default in five years. Bonds rated CCC have a 40% chance of default in five years. A portfolio consists of 30% B and 70% CCC-rated bonds. If a randomly selected bond defaults in a five-year period, what is the probability that it was a B-rated bond?
选项
A.0.625
B.0.211
C.0.429
D.0.250
答案
B
解析
According to Bayes' formula: P(B/default) = P(default and B)/P(default)P(default and B ) = P(default/B)×P(B) = 0.250×0.300 = 0.075P(default and CCC) = P(default/CCC)×P(CCC) = 0.400×0.700 = 0.280P(default) = P(default and B)+P(default and CCC) = 0.355P(B/default) = P(default and B)/P(default) = 0.075/0.355 = 0.211 根据贝叶斯公式：P(B/default) = P(default and B)/P(default) P(default and B ) = P(default/B)×P(B) = 0.250×0.300 = 0.075 P(default and CCC) = P(default/CCC)×P(CCC) = 0.400×0.700 = 0.280 P(default) = P(default and B)＋ P(default and CCC) = 0.355 P(B/default) = P(default and B)/P(default) = 0.075/0.355 = 0.211