154. An insurance company categorizes its policyholders into three mutually exclusive groups:
high-risk, medium-risk, and low-risk. An internal study of the company showed that 45% of the policyholders are low-risk and 35% are medium-risk. The probability of
death over the next year, given that a policyholder is high-risk is two times the
probability of death of a medium-risk policyholder. The probability of death over the
next year, given that a policyholder is medium-risk is three times the probability of death
of a low-risk policyholder. The probability of death of a randomly selected policyholder,
over the next year, is 0.009.
Calculate the probability of death of a policyholder over the next year, given that the
policyholder is high-risk.
(A) 0.0025
(B) 0.0200
(C) 0.1215
(D) 0.2000
(E) 0.3750
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