1. (b) Use the data in the following table, which summarizes results from 985 pe
ID: 3312594 • Letter: 1
Question
1. (b) Use the data in the following table, which summarizes results from 985 pedestrian deaths that were d aus by accidents (based on data from the National Highway Traffic Safety Administration) Driver intoxicated? Pedestrian Intoxicated? Yes No 59 266 No 79 581 i) Ifone ofthe pedestrian deaths is randomly selected find the probability that the pedestrian was intoxicated or the driver was intoxicated that the pedestrian was not intoxicated or the driver was not intoxicated. 13+3 points] disjonnt ; o.410/A?» :/sgt21+211, B5 40 9 065 9165 There is more test on the other sideExplanation / Answer
Solution:
We are given following information:
Driver Intoxicated?
Pedestrian Intoxicated?
Yes
No
Total
Yes
59
79
138
No
266
581
847
Total
325
660
985
Part i
We know
P(A or B) = P(A) + P(B) – P(A and B)
So,
P(Pedestrian intoxicated or driver intoxicated) = P(Pedestrian intoxicated) + P(driver intoxicated) – P(Pedestrian intoxicated and driver intoxicated)
P(Pedestrian intoxicated or driver intoxicated) = (325/985) + (138/985) – (59/985)
P(Pedestrian intoxicated or driver intoxicated) = (325 + 138 – 59) / 985 = 404/985 = 0.410152284
Required probability = 0.410152284
Part ii
We know
P(A or B) = P(A) + P(B) – P(A and B)
So,
P(Pedestrian not intoxicated or driver not intoxicated) = P(Pedestrian not intoxicated) + P(driver not intoxicated) – P(Pedestrian not intoxicated and driver not intoxicated)
P(Pedestrian not intoxicated or driver not intoxicated) = (660/985) + (847/985) – (581/985)
P(Pedestrian not intoxicated or driver not intoxicated) = (660 + 847 – 581) / 985
P(Pedestrian not intoxicated or driver not intoxicated) = 926/985 = 0.940101523
Required probability = 0.940101523
Driver Intoxicated?
Pedestrian Intoxicated?
Yes
No
Total
Yes
59
79
138
No
266
581
847
Total
325
660
985
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