
Probability and Statistics Basic Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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 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, 10:55 AM  #2 
Senior Member Joined: Jul 2012 From: DFW Area Posts: 635 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, 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 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
what is the topic of auto regresive in math?  craftindo  Linear Algebra  0  March 10th, 2014 05:39 PM 
Probability Problem / Insurance problem  bsjmath  Advanced Statistics  2  March 1st, 2014 02:50 PM 
Insurance Policy Problem  Camero  Advanced Statistics  2  December 31st, 2013 10:10 AM 
Auto Finance Formulas  mcsquared  Economics  1  November 8th, 2012 08:34 AM 
Autocensor on the boards  CRGreathouse  New Users  4  October 2nd, 2009 02:17 PM 