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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

Complement If A represents the event of randomly selecting one driver included in the table and getting someone who was not killed, what does A represent? Find the value of PA.

Short Answer

Expert verified

A represents the event of randomly selecting the driver who was killed in the head-on collision.

The value of PAis 0.445.

Step by step solution

01

Given information

The different categories in the table state the counts of drivers who met a head-on collision.

02

Define a complement event and its probability

A complementary event of an event E is represented by the symbol that expresses the idea that event E does not occur in the experiment.

The probability ofthe complementary event is stated below.

PE=1-PE

03

State the complementary event and probability

Add the sum total for the rows and columns.


Driver Killed

Driver Not killed

Total

Seatbelt Used

3655

7005

10660

Seatbelt not Used

4402

3040

7442

Total

8057

10045

18102

Define event A that a randomly selected driver was not killed in the collision.

As a result, A is the event that the randomly selected driver was killed in the passenger car.

04

Compute the probability 

The number of drivers who were not killed is 10045.

The total number of drivers is 18102.

The probability that the randomly selected driver was not killed is:

PA=1004518102=0.555

The probability that the randomly selected driver was killed is:

PA=1-PA=1-0.555=0.445

Thus, the complementary event has a probability of 0.445.

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