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27 August, 16:00

An insurance company believes that people can be divided into two classes: those who are accident prone and those who are not. The company's statistics show that an accident-prone person will have an accident at some time within a fixed 1-year period with probability 0.4, whereas this probability decreases to 0.2 for a person who is not accident prone.

1. If we assume that 30 percent of the population is accident prone, what is the probability that a new policyholder will have an accident within a year of purchasing a policy?

(a) 0.26

(b) 0.27

(c) 0.28

(d) 0.29

2. Given that a new policyholder has an accident within a year of purchasing a policy. What is the probability that she is accident prone?

(a) 4/13

(b) 5/13

(c) 6/13

(d) 7/13

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Answers (1)
  1. 27 August, 19:44
    0
    Step-by-step explanation:

    From the given information we can consolidate the given particulars as follows:

    People Accident prone Not accident prone

    100 30 70

    Prob for

    accident 0.4 0.2

    Joint persons 12 14 Total = 26

    1) Probability for a new policy holder to have accident=

    Prob he is accident prone and meets with accident + prob he is not accident prone but meets with accident

    = 0.26

    a is right

    2) Given he has an accident

    Prob she is accident prone = Prob accident prone and accident / 0.26

    = 0.12/0.26 = 6/13

    Option c
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