An insurance company believes that 30% of drivers are careless. The probability that a careless driver...

An insurance company believes that 30% of drivers are careless. The probability that a careless driver will have an accident in any one-year period is 0.4. The probability that a careful driver will have an accident in any one-year period is 0.2. Find the probability that a driver will have an accident next year given that she has had an accident this year.

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Expert Solution

P(accident )=P(careless and accident)+P(careful and accident)=0.3*0.4+0.7*0.2=0.26

therefore probability that a driver will have an accident next year given that she has had an accident this year

=P(accident next year|careless)*P(careless|accident)+P(accident next year|careful)*P(careful|accident)

=0.4*(0.3*0.4/0.26)+0.2*(0.7*0.2/0.26)=0.2923

orchestra answered 2 years ago

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