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September 10th, 2012, 12:51 AM   #1
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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.
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September 11th, 2012, 11:55 AM   #2
jks
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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%
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September 11th, 2012, 12:33 PM   #3
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Re: Probability Question - auto insurance

Nicely done!
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