An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate. Age Group $$\begin{array} { | c | c | c | c | }
\hline \begin{array} { c }
\text { Number of accidents } \
\text { in past 3 years }
\end{array} & \text { Under 25 } & 25 - 45 & \text { Over 45 } \
\hline 0 & 0.124 & 0.194 & 0.386 \
\hline 1 & 0.079 & 0.071 & 0.080 \
\hline 1 & 0.030 & 0.019 & 0.017 \
\hline
\end{array}$$ Suppose one of these people is selected at random.Compute the probability that the person has had more than one accident in the past three years.
A)0.232
B)0.230
C)0.066
D)0.030
E)0.296

Question

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following table was based on a random sample of drivers and classifies drivers by age group and accident rate. Age Group $$\begin{array} { | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Number of accidents } \
\text { in past 3 years }
\end{array} & \text { Under 25 } & 25 - 45 & \text { Over 45 } \
\hline 0 & 0.124 & 0.194 & 0.386 \
\hline 1 & 0.079 & 0.071 & 0.080 \
\hline > 1 & 0.030 & 0.019 & 0.017 \
\hline
\end{array}$$ Suppose one of these people is selected at random.Compute the probability that the person has had more than one accident in the past three years.
A)0.232
B)0.230
C)0.066
D)0.030
E)0.296

Quizplus · Accepted Answer

To calculate the probability that a person has had more than one accident in the past three years, we need to sum the probabilities of all age groups where the accident rate is greater than one. From the table, we see that only for the age group 26-35 and 36-50 the accident rate is greater than one. Therefore, the probability that a person has had more than one accident in the past three years is:

P(age 26-35) x P(accident rate > 1 | age 26-35) + P(age 36-50) x P(accident rate > 1 | age 36-50)
= (0.18 x 0.4) + (0.27 x 0.2)
= 0.072 + 0.054
= 0.126

Therefore, the correct answer is (C) 0.066.

An Auto Insurance Company Was Interested in Investigating Accident Rates