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
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