Assume that there are two types of drivers. The less safe drivers, who comprise 20% of the population, have probability 0.6 each of causing an accident in a year. The rest of the population are safe drivers, who have probability 0.1 each of causing an accident in a year. The insurance premium is $7000 times one’s probability of causing an accident in the coming year. Assume that for each driver, the events of causing an accident in different years are independent.
(a) What is the probability that a driver selected at random from the population will cause an accident in this year?
(b)A new subscriber had caused an accident this year. What is the probability that he/she is a less safe driver?
(c) How much should be the premium charged to the subscriber in part (b) for the following year?