How Do Insurance Risk Classes Affect Car Accident Probabilities?

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Insurance companies classify policyholders into four risk categories: excellent, good, average, and bad, each with distinct probabilities of being involved in a car accident over one year. The probabilities for these classifications are 0.02 for excellent risks, 0.05 for good risks, 0.14 for average risks, and 0.32 for bad risks. The distribution of policyholders is 8% excellent, 16% good, and 62% average, implying that a significant portion falls into the average and bad risk categories. To calculate the overall proportion of policyholders involved in accidents, one must consider the weighted probabilities based on the classification distribution. Additionally, the discussion seeks to determine the probability of a policyholder's classification given they did not have an accident in 2010, emphasizing the need for explicit event definitions.
agent2421
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Can someone please help me out with this problem.

1. In order to determine insurance premiums, suppose car insurance company classifies policyholders into 1 of 4 classes: excellent risks, good risks, average risks, and bad risks. Record probability will be excellent risk involved in car accident over 1 year span is 0.02, and then 0.05, 0.14 and 0.32 respectively for good, average and bad risk. Of its policy holders, 8% are classified as excellent risks, 16% are classified as good rsiks, and 62% are classified as average risks. You may assume car accidents are independent events.

A) What proportion of all polciyholders are involved in a car accident within a given one year period? Explictly define all events

B) If policyholder did not get into car accident during 2010, what is the probability they are classified as

I) Excellent risk
II) Good risk
III) Average risk
IV) Bad riks

Thanks.
 
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agent2421 said:
Explictly define all events
This is a good starting point. What are your events?

EDIT: Oh and welcome to PF!
 

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