試題詳解

316. A health insurance company classifies applicants, depending on their health, into one of three categories: A, B, or C.

The following probabilities apply:
i) P[A] = 5P[C]
ii) P[B] = 4P[C]
iii) P[ zero claims | A] = 0.1
iv) P[ zero claims | B] = 0.2
v) P[ zero claims | C] = 0.4

Calculate the probability that an insured was classified in category C, given that the insured had zero claims.
(A) 0.040
(B) 0.170
(C) 0.235
(D) 0.294
(E) 0.471