An insurance company believes that people can be divided into two classes: those who are accident...

An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. Their statistics show that an accident prone person will have an accident within a year with a probability of 0.4, whereas the probability for a nonaccident prone person is 0.2. It is assumed that 30% of the population is accident prone. Given that a new policyholder has an accident within a year of purchasing a policy, what is the probability that he or she is accident prone?

Expert Solution

Given,

P(Accident prone) = 0.30

So P(Not accident prone) = 1 - 0.30 = 0.70

P(Accident | Prone) = 0.4

P(Accident | Not prone) = 0.2

Hence by Bayes' theorem:

P(Prone | Accident)

= 6/13

= 0.4615

orchestra answered 2 years ago

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