Question
2. An auto insurance company classifies people into two classes, reckless (R) and non-reckless (~R) drivers. On the basis of prior experience, the company knows
2. An auto insurance company classifies people into two classes, reckless (R) and non-reckless (~R) drivers. On the basis of prior experience, the company knows that 1/5 of the population it insures are reckless drivers, while the rest are not. Through experience, the company knows that a reckless driver has a 3/5 chance of being in an accident (A) in a given year, but a non-reckless driver only has a 1/20 chance. If the company covers a new customer with no record, it assumes that there is a 1/5 chance that they are a reckless driver and so sets the rate accordingly. After one year, it is reasonable to modify the customer's premium rate on the basis of their driving record - if the driver is likely to be reckless, then the company will charge a higher premium. Within a year of buying insurance, Thuy ("Twee") has had one accident.
a) In the eyes of the auto insurance company, what is the probability that Thuy is a reckless driver given that she had an accident? (3 pts.)
b) Would it be wise for the insurance company to raise Thuy's premium? Why? (2 pts.)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started