Question

In Exercises 1–10, use the data in the accompanying table and express all results in decimal form. (The data are from “Mortality Reduction with Air Bag and Seat Belt Use in Head-On Passenger Car Collisions,” by Crandall, Olson, and Sklar, American Journal of Epidemiology, Vol. 153, No. 3.) Drivers Involved in Head-On Collision of Passenger Cars.

Drivers Involved in Head-On Collision of Passenger Cars

	Driver Killed	Driver Not killed
Seatbelt Used	3655	7005
Seatbelt not Used	4402	3040

Seatbelt Use If one driver is randomly selected, find the probability he or she was using a seatbelt

Short answer

The probability that the randomly selected driver uses a seatbelt is approximately 0.589.

Step-by-step solution

Given information

The data for drivers involved in a head-on collision is provided for passenger cars.

Step 2:Define the concept of probability

Probability is defined as the statistical measure that can be used to quantify the risk chances associated withany event.

Mathematically, it is the ratio of the favorable outcomes (to the event) and the total outcomes feasible.

Step 3:Compute the totals row-wise and column-wise in the table

The totals are computed as the additive sum of the row and column values as follows:

	Driver Killed	Driver Not killed	Total
Seatbelt Used	3655	7005	10660
Seatbelt not Used	4402	3040	7442
Total	8057	10045	18102

Compute the probability of an event

Define E as the event that a randomly selected driver uses a seatbelt.

The favorable number of drivers who use a seatbelt is 10660.

The total number of drivers surveyed is 18102.

The probability that a randomly selected driver uses a seatbelt is:

$$\begin{gathered} P\left(E\right)=\frac{10660}{18102} \\ =0.589 \end{gathered}$$

Thus, the probability that the randomly selected driver uses a seatbelt is 0.589.