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04fafin - Math 431 Final Exam Room B239 2:45pm 4:45pm Mrton...

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Math 431 Final Exam Room B239, 2:45pm - 4:45pm, December 18, 2004 M´arton Bal´azs NAME: 1. An insurance company runs a review on their payments, and reaches the following conclusions: 5% of policyholders had at least one accident in 2001, 5% of policyholders had at least one accident in 2002, and 5% of policyholders had at least one accident in 2003. 1% of policyholders had at least one accident in both 2001 and 2002, 1% of policyholders had at least one accident in both 2001 and 2003, and 1% of policyholders had at least one accident in both 2002 and 2003. 0.5% of policyholders had at least one accident in each 2001, 2002, and 2003. (a) (15 points) Compute the probability that a policyholder has at least one accident in 2002, given he/she had at least one in 2001. Is the probability of this policyholder having an accident in 2002 higher then the probability of the other policyholders having one in 2002? Are accidents of policyholders occurring independently in these two years?
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