My Math Forum Probability Question - auto insurance

 Probability and Statistics Basic Probability and Statistics Math Forum

 September 9th, 2012, 11:51 PM #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 12-month period is 0.02, while for a poor risk driver the probability of one or more accidents in a 12-month period is 0.10. a. Find the probability that a randomly chosen driver has an accident in a 12-month 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, 10:55 AM #2 Senior Member     Joined: Jul 2012 From: DFW Area Posts: 642 Thanks: 99 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*0.8-16 = 784 good risk drivers w/o accidents and 1000*0.2-20 = 180 bad risk drivers w/o accidents. So the probability is 784/(784+180) = 81.3%
 September 11th, 2012, 11:33 AM #3 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: Probability Question - auto insurance Nicely done!

 Tags auto, insurance, probability, question

,

,

,

,

,

,

,

,

,

,

,

# Insurance probability questions

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post craftindo Linear Algebra 0 March 10th, 2014 05:39 PM bsjmath Advanced Statistics 2 March 1st, 2014 02:50 PM Camero Advanced Statistics 2 December 31st, 2013 10:10 AM mcsquared Economics 1 November 8th, 2012 08:34 AM CRGreathouse New Users 4 October 2nd, 2009 02:17 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top