An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. The company's statistics show that an accident-prone person will have an accident at some time within a fixed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone.

1. If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy?

(a) 0.26

(b) 0.27

(c) 0.28

(d) 0.29

2. Given that a new policyholder has an accident within a year of purchasing a policy. What is the probability that she is accident prone?

(a) 4/13

(b) 5/13

(c) 6/13

(d) 7/13