Police are to conduct random breath testing on drivers on a busy road one Friday evening. Suppose
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Police are to conduct random breath testing on drivers on a busy road one Friday evening. Suppose 3% of the drivers drink and drive at the time. Let X be the number of drivers that police need to test to get the first case of drinking and driving. Let Y be the number of drivers tested to get 3 such cases.
(1) Find P(Y > 50).
(2) Suppose the police have not found any case of drinking and driving in their first 5 tests. What is the conditional probability that the police still cannot find any case in their next 5 tests?
(3) What is the probability that the police will find exactly 4 cases of drinking and driving in testing 200 drivers? At least two different probability distributions can be used to calculate/approximate this probability. Which two, and how different are the results?
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