In a large metropolitan area,one out of ten drivers on the road on Saturday after midnight is intoxicated.Half of all accidents during this time period involve drunk drivers.Finally,the overall accident rate on Saturday after midnight is 3 accidents per 100 cars on the road.For a drunk driver,the risk of accident is _____.
A)1/10
B)1/2
C)3/100
D)3/20
E)1/100

Question

Quizplus · Accepted Answer

If one out of ten drivers is intoxicated, then the probability of a driver NOT being intoxicated is 9/10. The probability of an accident involving a drunk driver is 1/2. Therefore, the overall probability of an accident involving a driver on Saturday after midnight is:
(1/10)(1/2) + (9/10)(1/100) = 1/20 + 9/1000 = 53/1000
The probability of an accident for a drunk driver can be found using Bayes' theorem:
P(accident | drunk) = P(drunk | accident) * P(accident) / P(drunk)
P(drunk | accident) = (1/2) (given in the problem)
P(accident) = 3/100 (given in the problem)
P(drunk) = 1/10 (given in the problem)
P(accident | drunk) = (1/2) * (3/100) / (1/10) = 3/20. 
Therefore, the risk of accident for a drunk driver is 3/20 or 15/100. The best choice is D.

In a Large Metropolitan Area,one Out of Ten Drivers on the Road