Please show work, I need the visual! Thanks An insurance company believes that p
ID: 3352711 • Letter: P
Question
Please show work, I need the visual! Thanks
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 population 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?Explanation / Answer
Here,
Pr(accident occur for an accident prone person) = 0.3
Pr(accident occur for an non-accident prone person) = 0.2
Pr(accident prone) = 0.1
Pr(non accident prone) = 1 - 0.1 = 0.9
(a) Pr(accident will happen) = Pr(accident prone) * Pr(accident occur for an accident prone person) + Pr(non accident prone) * Pr(accident occur for an non-accident prone person)
= 0.1 * 0.3 + 0.9 * 0.2 = 0.21
(b) Pr(accident prone l had an accident withing a year of purchasing a policy) = (0.1 * 0.3)/ 0.21 = 1/7 = 0.1429