A study was recently done that emphasized the problem we all face with drinking and driving. Four hundredaccidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehiclesinvolved and whether alcohol played a role in the accident. The numbers are shown below. Given that anaccident involved multiple vehicles, what is the probability that it involved alcohol? $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Number of Vehicles Involved } $
$\begin{array} { r | c c c | c }
\text { Did Alcohol Play a Role? } & 1 & 2 & 3 \text { or more } & \text { Totals } \
\hline \text { Yes } & 55 & 94 & 21 & 170 \
\text { No } & 25 & 170 & 35 & 230 \
\hline \text { Totals } & 80 & 264 & 56 & 400
\end{array}$
A) $\frac { 23 } { 64 }$
B) $\frac { 23 } { 80 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 21 } { 400 }$

Question

A study was recently done that emphasized the problem we all face with drinking and driving. Four hundredaccidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehiclesinvolved and whether alcohol played a role in the accident. The numbers are shown below. Given that anaccident involved multiple vehicles, what is the probability that it involved alcohol? $\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\quad $$\text { Number of Vehicles Involved } $
$\begin{array} { r | c c c | c } 
\text { Did Alcohol Play a Role? } & 1 & 2 & 3 \text { or more } & \text { Totals } \
\hline \text { Yes } & 55 & 94 & 21 & 170 \
\text { No } & 25 & 170 & 35 & 230 \
\hline \text { Totals } & 80 & 264 & 56 & 400
\end{array}$
A) $\frac { 23 } { 64 }$
B) $\frac { 23 } { 80 }$
C) $\frac { 3 } { 8 }$
D) $\frac { 21 } { 400 }$

Quizplus · Accepted Answer

The probability that an accident involved alcohol given it involved multiple vehicles is calculated by dividing the number of multi-vehicle accidents involving alcohol by the total number of multi-vehicle accidents. Multi-vehicle accidents are those involving 2 or 3 or more vehicles. From the table, the number of accidents involving alcohol with 2 vehicles is 94, and with 3 or more vehicles is 21, making a total of 115 accidents involving alcohol and multiple vehicles. The total number of multi-vehicle accidents is 264 (2 vehicles) + 56 (3 or more vehicles) = 320. Therefore, the probability is $ \frac{115}{320} = \frac{23}{64} $.

A Study Was Recently Done That Emphasized the Problem We \quad

A Study Was Recently Done That Emphasized the Problem We $\quad$