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Probability

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

In the secretary problem, assuming that we reject the first n/2 candidates, and after
that pick the first candidate who is better than all but at most two of the candidates
interviewed. Whenever needed you can assume that n is sufficiently large. What is
the probability to hire one of the top 10 candidates? Don’t try to compute the exact
probability, but try to give a good lower bound on this probability.

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In the Introduction to Impossibility module, 4/5 of students pass the exam. Of those who pass the exam 9/10 attend lectures, and of those who fail only 1/2 attend lectures. What is the probability that a student who doesn’t attend lectures passes the exam?
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A factory received a shipment of 49 generators, and the vendor who sold the items knows there are 7 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment.For each of the following, give your responses as a fraction or rounded to 4 decimal places.If a sample of 4 generators is selected, find the probability that all in the sample are defective. If a sample of 7 generators is selected, find the probability that none in the sample are defective.
Events A and B are mutually exclusive. Suppose event A Occurs with probability 0.58 and event B occurs with probability 0.32. Compute the following. (If necessary, consult a list of formulas.) (a) Compute the probability that B occurs but A does not occur. (b) Compute the probability that neither the event A nor the event B occurs.