An auto insurance company insures drivers of all ages. An actuary compiled the following statistics on the company’s insured drivers: Age of Driver Probability of Accident Portion of Company’s Insured Drivers 16-20 21-30 31-65 66-99 0.06 0.03 0.02 0.04 0.08 0.15 0.49 0.28 A randomly selected driver that the company insures has an accident. Calculate the probability that the driver was age 16-20.

Answer:0.16Step-by-step explanation:You can use the Bayes theorem, it lets you calculate the probability of occurrence of an event knowing that others happened before and the probability of other events.Labeling the events.A= A driver has an accidentB,C,D,E= The driver´s age is between 16-20, 21-30, 31-65 and 66-99 respectively. In this case the bayes theorem is :[tex]P(B|A)=\frac{P(A|B)P(B)}{P(A|B)P(B)+P(A|C)P(C)+P(A|D)P(D)+P(A|E)P(E)}[/tex] The probabilities are:P(B)= 0.08P(C)=0.15P(D)=0.49P(E)=0.28P(A|B)=0.06P(A|C)=0.03P(A|D)=0.02P(A|E)=0.04Calculating:[tex]P(B|A)=\frac{0.06*0.08}{0.06*0.08+0.03*0.15+0.02*0.49+0.04*0.28}=0.1584[/tex]Aproximately 0.16