An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years. Age Group $$\begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Number of accidents } \ \text { in past 3 years } \end{array} & 45 & \text { Total } \ \hline 0 & 98 & 145 & 296 & 539 \ \hline 1 & 60 & 70 & 77 & 207 \ \hline 1 & 22 & 5 & 2 & 29 \ \hline \text { Total } & 180 & 220 & 375 & 775 \ \hline \end{array}$$ If one of these drivers is selected at random,find the probability that the person has had no accidents in the last three years or is younger than 25. A)0.928 B)0.126 C)0.544 D)0.182 E)0.801

Question

An auto insurance company was interested in investigating accident rates for drivers in different age groups.The following contingency table was based on a random sample of drivers and classifies drivers by age group and number of accidents in the past three years. Age Group $$\begin{array} { | c | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Number of accidents } \
\text { in past 3 years }
\end{array} & < 25 & 25 - 45 & > 45 & \text { Total } \
\hline 0 & 98 & 145 & 296 & 539 \
\hline 1 & 60 & 70 & 77 & 207 \
\hline > 1 & 22 & 5 & 2 & 29 \
\hline \text { Total } & 180 & 220 & 375 & 775 \
\hline
\end{array}$$ If one of these drivers is selected at random,find the probability that the person has had no accidents in the last three years or is younger than 25.
A)0.928
B)0.126
C)0.544
D)0.182
E)0.801

Quizplus · Accepted Answer

To find the probability that the person has had no accidents in the last three years or is younger than 25, we add the probability of having no accidents (regardless of age) to the probability of being younger than 25 (regardless of accident history), subtracting the overlap (those younger than 25 who had no accidents, since they are counted in both groups).Probability of no accidents = 539/775Probability of being younger than 25 = 180/775Overlap (younger than 25 and no accidents) = 98/775So, the combined probability = (539 + 180 - 98) / 775 = 621 / 775 = 0.801.

An Auto Insurance Company Was Interested in Investigating Accident Rates