A car insurance company insures four types of drivers: () Good drivuot; who hnge

Question

A car insurance company insures four types of drivers: () Good drivuot; who hnge, aa 1 % chauce of Pei,ting in an aciIKIent each year Mediocre drivers have a 5% chance of getting in an accident in each year Atrocious drivers who have a 35% chance of getting in an accident in each year ·Ludicrously bad drivers who have a 90% chance of getting in an accident each year 50% of drivers are good, 35% are mediocre, 12% are atrocious, and 3% are ludicrously bad. A driver they insure gets in an accident, what is the likelihood he is a good, mediocre, atrocious, or ludicrously bad driver.

Explanation / Answer

probability of driver get in an accident

=P(good driver and gets in accident+mediocre driver and gets in accident+atrocious driver and gets in accident+ludicrously driver and gets in accident)

=0.5*0.01+0.35*0.05+0.12*0.35+0.03*0.9 =0.0915

a) hence P(good|get into accident) =P(good driver and gets in accident)/P(get into accident)

=0.5*0.01/0.0915 =0.0546

b)

P(mediocre|get into accident) =P(mediocre driver and gets in accident)/P(get into accident)

=0.35*0.05/0.0915 =0.1913

c)

P(atrocious|get into accident) =P(atrocious driver and gets in accident)/P(get into accident)

=0.12*0.35/0.0915 =0.4590

d)

P(ludicrous|get into accident) =P(ludicrous driver and gets in accident)/P(get into accident)

=0.03*0.9/0.0915 =0.2951

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