Your automobile insurance company uses past history to determine how to set rates by measuring the number of accidents caused by clients in various age ranges. The following table summarizes the proportion of those insured and the corresponding probabilities by age range:
Table4.6.5.Age vs Accident Likelihood
Age
Proportion of Insured
Probability of Accident
16-20
0.05
0.08
21-25
0.06
0.07
26-55
0.49
0.02
55-65
0.25
0.03
over 65
0.15
0.04
One of your family friends insured by this company has an accident.
Determine the conditional probability that the driver was in the 16-20 age range.
Compare this to the probability that the driver was in the 18-20 age range. Discuss the difference.
Determine how much more the company should charge for someone in the 16-20 age range compared to someone in the 26-55 age range.