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Traffic FatalitiesThe following data represent the number
Chapter 5, Problem 19E(choose chapter or problem)
Problem 19E
Traffic FatalitiesThe following data represent the number of traffic fatalities in the United States in 2009 by seat location and gender.
|
Male |
Female |
Total |
Driver |
32,873 |
11,856 |
44,729 |
Passenger |
6,453 |
6,363 |
12,816 |
Total |
39,326 |
18,219 |
57,545 |
(a) Among female fatalities, what is the probability that a randomly selected fatality is the driver?
(b) Among passenger fatalities, what is the probability that a randomly selected fatality is female?
(c) Suppose you are a police officer called to the scene of a traffic accident with a fatality. The dispatcher states that the victim was driving, but the gender is not known. Is the victim more likely to be male or female? Why?
Questions & Answers
QUESTION:
Problem 19E
Traffic FatalitiesThe following data represent the number of traffic fatalities in the United States in 2009 by seat location and gender.
|
Male |
Female |
Total |
Driver |
32,873 |
11,856 |
44,729 |
Passenger |
6,453 |
6,363 |
12,816 |
Total |
39,326 |
18,219 |
57,545 |
(a) Among female fatalities, what is the probability that a randomly selected fatality is the driver?
(b) Among passenger fatalities, what is the probability that a randomly selected fatality is female?
(c) Suppose you are a police officer called to the scene of a traffic accident with a fatality. The dispatcher states that the victim was driving, but the gender is not known. Is the victim more likely to be male or female? Why?
ANSWER:
Solution :
Step 1 of 3:
Consider the number of traffic fatalities table is given below,
Male |
Female |
Total |
|
Driver |
32873 |
11856 |
44729 |
Passenger |
6453 |
6363 |
12816 |
Total |
39326 |
18219 |
57545 |
Our goal is :
a). We need to find the probability that the driver, among female fatalities.
b). We need to find the probability that the driver, among male fatalities
c). We need to find is the victim more likely to be male or female.
a). Let F denotes the selected fatality is the driver.
Let E denotes the female fatalities.
The probability of occurrence of the event F given the occurrence of event E is
P=
Among female fatalities, the probability that the driver is
P=
P= 0.6507
Therefore, the probability that the driver is 0.6507.