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Math Help - Insurance premiums and probability.

  1. #1
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    Post Insurance premiums and probability.

    In order to determine insurance premiums, suppose that a car insurance company classifies policyholders
    into one of four classes: excellent risks, good risks, average risks, and bad risks. Their records indicate that
    the probability an excellent risk individual will be involved in a car accident over a one-year span is 0.02.
    The same probability for good, average, and bad risk individuals are, respectively, 0.05, 0.14, and 0.32. Of
    its policy holders, 8% are classified as excellent risks, 16% are classified as good risks, and 62% are
    classified as average risks. You may assume that car accidents are independent events.
    (A) What proportion of all policyholders are involved in a car accident within a given one-year period? You
    must explicitly define all events.
    (B) If a policyholder did not get into a car accident during 2010, what is the probability they are classified as
    (i) an excellent risk? (ii) a good risk? (iii) an average risk? (iv) a bad risk?
    Last edited by mr fantastic; October 19th 2011 at 04:37 AM. Reason: Re-titled.
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    Re: Insurance premiums and probability.

    Quote Originally Posted by jakeroy17 View Post
    In order to determine insurance premiums, suppose that a car insurance company classifies policyholders
    into one of four classes: excellent risks, good risks, average risks, and bad risks. Their records indicate that
    the probability an excellent risk individual will be involved in a car accident over a one-year span is 0.02.
    The same probability for good, average, and bad risk individuals are, respectively, 0.05, 0.14, and 0.32. Of
    its policy holders, 8% are classified as excellent risks, 16% are classified as good risks, and 62% are
    classified as average risks. You may assume that car accidents are independent events.
    (A) What proportion of all policyholders are involved in a car accident within a given one-year period? You
    must explicitly define all events.
    (B) If a policyholder did not get into a car accident during 2010, what is the probability they are classified as
    (i) an excellent risk? (ii) a good risk? (iii) an average risk? (iv) a bad risk?
    I sugest you first calculate what percentage of policy holders are bad risks.
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