Travel and Transportation. Some researchers believe that the severity of an auto

Question

Travel and Transportation. Some researchers believe that the severity of an automobile accident is related to the type of vehicle. For example, pickup trucks tend to be involved in more fatal crashes than other types of vehicles. The following table presents the number of vehicles involved in each type of crash. Suppose this table is representative of all crashes in the United States and one crash is selected at random.

(a) What is the probability (± ± 0.0001) that the crash results in injury only?

P(Injury) P(Injury) =

(b) Suppose the crash involves a utility vehicle. What is the probability (± ± 0.0001) that it is fatal?

P(Fatal | Utility) P(Fatal | Utility) =

(c) Suppose the crash involves property damage only. What is the probability (± ± 0.0001) that the vehicle is a large truck?

P(Large | Property) P(Large | Property) =

(d) Suppose the crash is not fatal. What is the probability (± ± 0.0001) that it involves a bus?

P(Bus | Not Fatal) P(Bus | Not Fatal) =

(e) Suppose the crash does not involve a passenger car. What is the probability (± ± 0.0001) that it results in injury only?

P(Injury | Not passenger) P(Injury | Not passenger) =

(f) Are the events fatal crash and van independent?

Dependent

Independent

(g) Suppose two crashes are selected at random. What is the probability (± ± 0.0001) that both were fatal and involved an unknown type of vehicle?

P(Both fatal and unknown vehicle) P(Both fatal and unknown vehicle) = ______ ×107

Fatal Crash Injury Property Total Passenger Car 18350 1506595 3686062 5211007 Pick up 8452 376156 1001893 1386501 Utility 6924 447946 1187911 1642781 Van 2494 174299 453197 629990 Other Light 32 67828 222940 290800 Large Truck 3215 53411 239298 295924 Bus 221 9968 47387 57576 Other Light 1152 6282 12429 19863 Total 40840 2642485 6851117 9534442

Explanation / Answer

Solution:

a) P(injury) = 2642485/9534442 = 0.2772

b) P(Fatal | Utility) = (6924/9534442)/(1642781/9534442) = 0.00421

c) P(Large | Property) = 239298/6851117 = 0.0349

d) P(Bus | Not Fatal) = 1-(221/40840) = 0.9946

e) P(Injury | Not passenger) = 1- ( 264285/5211007) = 0.9493

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