An insurance company believes that people can be divided into two classes -- those that are accident prone and those that are not. Their statistics show that an accident-prone person will have an accident at some time within a fixed 1-year period with probability 0.3, whereas this probability decreases to 0.2 for a non-accident-prone person. Assume that 10 percent of the populations is accident prone.
(a) What is the probability that a new policy holder will have an accident within a year of purchasing a policy?
(b) Suppose a new policy holder has an accident within a year of purchasing a policy. What is the probability that he or she is accident prone?
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