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.)