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September 10th, 2012, 12:51 AM  #1 
Senior Member Joined: Sep 2011 From: New York, NY Posts: 333 Thanks: 0  Probability Question  auto insurance
An automobile insurance company classifies drivers as either good risks or poor risks. They believe that good risks constitute 80% of the drivers who apply to them for insurance are good risks, while 20% are not. The probability that a good risk driver will have one or more accidents in any 12month period is 0.02, while for a poor risk driver the probability of one or more accidents in a 12month period is 0.10. a. Find the probability that a randomly chosen driver has an accident in a 12month period. b. If a driver has an accident within 12 months of buying an insurance policy, find the probability that he or she is a good risk driver. c. If a driver does NOT have an accident within 12 months of buying an insurance policy, find the probability that he is a good risk driver. 
September 11th, 2012, 11:55 AM  #2 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 634 Thanks: 96 Math Focus: Electrical Engineering Applications  Re: Probability Question  auto insurance
Probability is not my strong suit, but I will give it a try: a. Assume 1000 drivers. On average there will be 1000*0.8*0.02 = 16 good risk drivers with accidents. There will be 1000*0.2*0.1 = 20 bad risk drivers with accidents. So 16 + 20 = 36 drivers out of 1000 will have accidents. 36/1000 = 3.6% b. Out of the 36 drivers with accidents, 16 will be good risk drivers (from a. above). So the probability is 16/36 = 4/9 = 44.4%. c. There are 1000*0.816 = 784 good risk drivers w/o accidents and 1000*0.220 = 180 bad risk drivers w/o accidents. So the probability is 784/(784+180) = 81.3% 
September 11th, 2012, 12:33 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Probability Question  auto insurance
Nicely done!


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