An insurance company believes that drivers can be divided into two classes, those that are of high risk and those that are of low risk. Their statistics show that a high-risk driver will have an accident at some time within a year with probability 0.4, but this probability is only 0.1 for low-risk drivers. Assume 20% of the drivers are high-risk. If a new policy holder does not have any accident within a year of purchasing a policy, what is the probability that he is a low-risk type driver? (round your answer to 3 decimal places) O 0.857 O 0.500 O 0.160 O 0.143

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An insurance company believes that drivers can be divided into two classes, those that are of high
risk and those that are of low risk. Their statistics show that a high-risk driver will have an accident
at some time within a year with probability 0.4, but this probability is only 0.1 for low-risk drivers.
Assume 20% of the drivers are high-risk.
If a new policy holder does not have any accident within a year of purchasing a policy, what is the
probability that he is a low-risk type driver? (round your answer to 3 decimal places)
O 0.857
O 0.500
O 0.160
O 0.143
Transcribed Image Text:An insurance company believes that drivers can be divided into two classes, those that are of high risk and those that are of low risk. Their statistics show that a high-risk driver will have an accident at some time within a year with probability 0.4, but this probability is only 0.1 for low-risk drivers. Assume 20% of the drivers are high-risk. If a new policy holder does not have any accident within a year of purchasing a policy, what is the probability that he is a low-risk type driver? (round your answer to 3 decimal places) O 0.857 O 0.500 O 0.160 O 0.143
Expert Solution
Step 1

We use Bayes theorem to solve this problem.

Given high risk drivers are 20% and their risk probability is 0.4

Given low risk drivers are 80% and their risk probability is 0.1

 

 

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