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Please help with P type question

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  • Please help with P type question

    A family health insurance policy pays the total of the first three claims per year. If there is one claim during the year, the amount claimed is uniformly distributed between 100 and 500. If there are 2 claims in the year, the total amount claimed is uniformly distributed between 200 and 1000, and if there are 3 claims in the year, the total amount claimed is uniformly distributed between 500 and 2000. The probabilities of 0, 1, 2, and 3 claims in the year are 0.5, 0.3, 0.1, 0.1 respectively. Find the probability that the insurer pays at least 500 in total claims for the year.

    If anyone knows how to solve this, please reply.

  • #2
    To get you started-

    P (atleast 500) = 1 - P(less than 500)

    How can total claim amt be less than 500? Take different cases-

    1) no claims

    2) 1 claim

    3) 2 claims and total claim amt is between 200-500

    Add the probabilities of these 3 cases to get the answer.

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    • #3
      solution to your question.

      I think this is an application of baye's theorem.

      Let X represent the amount of the claim, and let 1, 2, 3, represent the number of claims.

      Therefore, we want P(X>=500) = P(X>=500|1)P(1) + P(X>=500)|2)P(2) + P(X>=500|3)P(3)

      Now, each of the above terms is easy to calculuate since we know how each claim amount is distributed.

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      • #4
        I figured it out..thanks

        Thank you to both of you who replied so quickly. My problem was trying to figure out the probablity for each and the solution finally hit me over head like a brick : )) I couldn't figure out where the probability numbers came from but I've got it now.

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