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In Exercises 1鈥10, use the data in the accompanying table and express all results in decimal form. (The data are from 鈥淢ortality Reduction with Air Bag and Seat Belt Use in Head-On Passenger Car Collisions,鈥 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

Expert verified

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

Step by step solution

01

Given information

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

02

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.

03

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

04

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:

PE=1066018102=0.589

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

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