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Help with Probability question.

  1. Feb 17, 2012 #1
    So I've been trying to do probability problems to take the P/1 Exam, and I've come across a problem that I don't quite understand.


    An insurance company estimates that 40% of policyholders who have only an auto policy
    will renew next year and 60% of policyholders who have only a homeowners policy will
    renew next year. The company estimates that 80% of policyholders who have both an
    auto and a homeowners policy will renew at least one of those policies next year.
    Company records show that 65% of policyholders have an auto policy, 50% of
    policyholders have a homeowners policy, and 15% of policyholders have both an auto
    and a homeowners policy. Using the company’s estimates, calculate the percentage of
    policyholders that will renew at least one policy next year.

    Attempt at solution:

    Pr(A ∩ H(compliment)) = Pr(A - H) = Pr(A) - Pr(H)

    Pr(A) = .65
    Pr(H) = .50

    .65 - .50 = .15

    However, the solution claims that Pr(A - H) = Pr(A-(A ∩ H)) = .50. How is that possible? How did they derive that?

    Edit: Disregard, I understand it now. I had to apply the Pr(A U B) = Pr(A) + Pr(B) - Pr(A ∩ B) rule.
    Last edited: Feb 17, 2012
  2. jcsd
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