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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 using a seatbelt, what does A represent? Find the value of PA.

Short Answer

Expert verified

A represents the event of randomly selecting the driver who did not use a seatbelt.

The value of PAis 0.411.

Step by step solution

01

Given information

The counts of drivers involved in a head-on collision are categorized.

02

Define a complement event and its probability

A complementary event denoted as E for any arbitrary event E is defined as the event of the non-occurrence of event E.

If E has a probability PE, then the complementary event has a probability as follows:

PE=1-PE

03

Define a complementary event with reference to the study

The totals are computed for each row and column.


Driver Killed

Driver Not killed

Total

Seatbelt Used

3655

7005

10660

Seatbelt not Used

4402

3040

7442

Total

8057

10045

18102

Define event Aas a randomly selected driver from 18102 uses seatbelt.

The complementary event of A is the non-occurrence of A.

Thus, is the event that the randomly selected driverdoes not use a seatbelt.

04

Compute the probability 

The number of drivers who use seatbelts is 10660.

The number of drivers in the study is 18102.

Thus, the probability of event A is computed as follows:

PA=1066018102=0.589

The probability of the complementary event is obtained as follows.

PA=1-PA=1-0.589=0.411

Thus, the complementary event has a probability of 0.411.

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