In a certain year, 44.9% 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? (Round your answer to four decimal places.)

To find the probability that the victim of a deadly side-impact accident was driving a car, we can use **Bayes' Theorem** or a related approach, where we consider the proportion of vehicles and the probabilities of deadly accidents associated with them.

Let's break down the given information:

- 44.9% of all light vehicles are cars, so the probability that a vehicle is a car is:
  \[
  P(\text{Car}) = 0.449
  \]
  
- The rest of the vehicles are pickups or SUVs, meaning:
  \[
  P(\text{Pickup or SUV}) = 1 - 0.449 = 0.551
  \]

Next, we need to know two additional things to solve the problem:
1. **The probability that a deadly side-impact accident occurs while driving a car** \(P(\text{Deadly | Car})\).
2. **The probability that a deadly side-impact accident occurs while driving a pickup or SUV** \(P(\text{Deadly | Pickup or SUV})\).

These probabilities are typically provided in the table. Once we have them, the problem becomes one of conditional probability, specifically:

\[
P(\text{Car | Deadly}) = \frac{P(\text{Deadly | Car}) \cdot P(\text{Car})}{P(\text{Deadly})}
\]

Where \( P(\text{Deadly}) \) is the overall probability that a vehicle involved in a deadly side-impact accident is either a car or a pickup/SUV. This can be calculated using the law of total probability:

\[
P(\text{Deadly}) = P(\text{Deadly | Car}) \cdot P(\text{Car}) + P(\text{Deadly | Pickup or SUV}) \cdot P(\text{Pickup or SUV})
\]

Once you provide the values for \( P(\text{Deadly | Car}) \) and \( P(\text{Deadly | Pickup or SUV}) \) from the table, I can perform the calculation to determine the final probability.

Would you like to proceed with this or provide those missing values?

Learn how to use Bayes' Theorem and conditional probability to calculate the probability that a deadly side-impact crash victim was driving a car. The problem involves key concepts in probability theory, including Bayes' Theorem and the law of total probability, and is suitable for students in Grades 11-12 or college level.

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