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 $180220375775\begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } \text { Number of accidents } \\\text { in past 3 years }\end{array} & < 25 & 25 - 45 & > 45 & \text { Total } \\\hline 0 & 98 & 145 & 296 & 539 \\\hline 1 & 60 & 70 & 77 & 207 \\\hline > 1 & 22 & 5 & 2 & 29 \\\hline \text { Total } & 180 & 220 & 375 & 775 \\\hline\end{array}$ 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

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 45 & ext { Total } \\hline 0 & 98 & 145 & 296 & 539 \\hline 1 & 60 & 70 & 77 & 207 \\hline > 1 & 22 & 5 & 2 & 29 \\hline ext { Total } & 180 & 220 & 375 & 775 \\hline\end{array}> Number of accidents in past 3 years < 25 25 − 45 > 45 Total 0 98 145 296 539 1 60 70 77 207 > 1 22 5 2 29 Total 180 220 375 775 \begin{array} { | c | c | c | c | c | } \hline \begin{array} { c } ext { Number of accidents } \ ext { in past 3 years }\end{array} & < 25 & 25 - 45 & > 45 & ext { Total } \\hline 0 & 98 & 145 & 296 & 539 \\hline 1 & 60 & 70 & 77 & 207 \\hline > 1 & 22 & 5 & 2 & 29 \\hline ext { Total } & 180 & 220 & 375 & 775 \\hline\end{array} Number of accidents in past 3 years 0 1 > 1 Total < 25 98 60 22 180 25 − 45 145 70 5 220 > 45 296 77 2 375 Total 539 207 29 775 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) 0.928B) 0.126C) 0.544D) 0.182E) 0.801

Zybrea Knight · Accepted Answer

Final Answer : E, Explanation :  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.

Definitions

Learning Objectives

Learning Objectives

Related questions