How Do Insurance Risk Classes Affect Car Accident Probabilities?

[agent2421]

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.

 

[spamiam]

Explictly define all events

This is a good starting point. What are your events?

EDIT: Oh and welcome to PF!