ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers wh
ID: 3341011 • Letter: A
Question
ABC Auto Insurance classifies drivers as good, medium, or poor risks. Drivers who apply to them for insurance fall into these three groups in the proportions 30%, 50%, and 20%, respectively. The probability a “good” driver will have an accident is .01, the probability a “medium” risk driver will have an accident is .03, and the probability a “poor” driver will have an accident is .10. The company sells Mr. Brophy an insurance policy and he has an accident. What is the probability Mr. Brophy is: a. A “good” driver? (Round your answers to 3 decimal places.) Probability b. A “medium” risk driver? (Round your answers to 3 decimal places.) Probability c. A “poor” driver? (Round your answers to 3 decimal places.) Probability
Explanation / Answer
Ans:
Given that
P(good)=0.3
P(medium)=0.5
P(poor)=0.2
P(accident/good)=0.01
P(accident/medium)=0.03
P(accident/poor)=0.1
First find P(accident):
P(accident)=P(accident/good)*P(good)+P(accident/medium)*P(medium)+P(accident/poor)*P(poor)
=0.3*0.01+0.5*0.03+0.2*0.1
=0.003+0.015+0.02=0.038
a)P(good/accident)=P(accident/good)*P(good)/P(accident)
=(0.3*0.01)/0.038=0.003/0.038=0.079
b)P(medium/accident)=P(accident/medium)*P(medium)/P(accident)
=(0.5*0.03)/0.038=0.015/0.038=0.395
c)P(poor/accident)=P(accident/poor)*P(poor)/P(accident)
=(0.2*0.1)/0.038=0.02/0.038=0.526