
#1
Feb1712, 10:52 AM

P: 6

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.
Problem: 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. 


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