**Example**

**Example**- An insurance company that believes that people can be divided inot two distinct
classes -- those who are accident prone and those who are not. During any given
year an accident-prone person will have an accident with probability .4, whereas
the corresponding figure for a non-accident-prone person is .2.
**(a)**If we assume that 30 percent of the population is accident phone, what is the probability that a new policyholder whill have an accident within a year of purchasing a policy?

**(b)**What is the conditional probability that a new policyholder will have an accident in his or her second year of policy ownership, given that the policyholder has had an accident in the first year?

We shall obtain the desired probability by first conditioning upon whether or not the policyholder is accident prone. Let

If we let

Now,

However,