In 2001, 37.4% of all light vehicles were cars, and the rest were pickups or SUVs. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table. What is the probability that the victim of a deadly side-impact accident was driving a car Please, round your answer to two decimal places. $\begin{array} { | l | l | }
\hline \text { Cars } & 1.0 \
\hline \text { Light Truck or SUV } & 0.3 \
\hline
\end{array}$

Question

In 2001, 37.4% of all light vehicles were cars, and the rest were pickups or SUVs. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table. What is the probability that the victim of a deadly side-impact accident was driving a car  Please, round your answer to two decimal places. $\begin{array} { | l | l | } 
\hline \text { Cars } & 1.0 \
\hline \text { Light Truck or SUV } & 0.3 \
\hline
\end{array}$

Quizplus · Accepted Answer

To find the probability that the victim of a deadly side-impact accident was driving a car, we use Bayes' theorem or a basic probability approach. The probability of dying in a side-impact crash if driving a car is 1.0, and for light trucks or SUVs, it's 0.3. Given that 37.4% of vehicles are cars, 62.6% are light trucks or SUVs. The weighted probability of dying in a side-impact crash, considering the distribution of vehicle types, is $0.374 \times 1.0 + 0.626 \times 0.3$. The probability that a deadly accident victim was in a car is the fraction of car-related deaths over total deaths, which is $\frac{0.374}{0.374 + 0.626 \times 0.3}$, resulting in approximately 0.67 when calculated and rounded to two decimal places.

In 2001, 37 Cars 1.0 Light Truck or SUV 0.3\begin{array} { | l | l | } \hline \text { Cars } & 1.0 \\\hline \text { Light Truck or SUV } & 0.3 \\\hline\end{array} Cars Light Truck or SUV ​1.00.3​​

In 2001, 37 $\begin{array} { | l | l | } \hline \text { Cars } & 1.0 \\\hline \text { Light Truck or SUV } & 0.3 \\\hline\end{array}$