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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1 Here Y is the number of drivers tested to get 3 such cases Here as we have to find PY 50 Probabili... View the full answer