Question

2. Bayes) Suppose an automobile insurance company classifies a driver as good, average, or bad. Of all their insured drivers, 25% are classified good, 50% are average, and 25% are bad. Suppose for the coming year, a good driver has a 5% chance of having an accident, and average driver has 15% chance of having an accident, and a bad driver has a 25% chance. If you had an accident in the past year what is the probability that you are a good driver?

Answer 1

SOLUTION-

Given,

P(good)=0.25

P(average)=0.50

P(bad)=0.25

P(accident/good)=0.05

P(accident/average)=0.15

P(accident/bad)=0.25

Now,

P(accident)=P(accident/good)*P(good)+P(accident/average)*P(average)+P(accident/bad)*P(bad)

=0.05*0.25+0.15*0.50+0.25*0.25

=0.15

Now,

P(good/accident)=P(accident/good)*P(good)/P(accident)

=0.05*0.25/0.15

=0.0833

IF YOU HAVE ANY DOUBT PLEASE COMMENT DOWN BELOW I WILL SOLVE IT FOR YOU:)
----------------PLEASE RATE THE ANSWER-----------THANK YOU!!!!!!!!----------