Unformatted text preview: SIEO 3600 (IEOR Majors) Practice Problem Set #1 Introduction to Probability and Statistics February 10, 2010 Practice Problem Set #1 1. Five independent flips of a fair coin are made. Find the probability that (a) the first three flips are the same; (b) either the first three flips are the same, or the last three flips are the same; (c) there are at least two heads among the first three flips, and at least two tails among the last three flips. 2. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. What are the possible values of X ? 3. Columbia University has studied the percentage of spam e-mail that the Columbia community receives every day, and it has determined that 60% of the e-mail is spam. The university has designed a computer program to identify whether a specific e-mail is spam or not. If an e-mail is spam, the probability that the program will classify it as “spam” is 0.8, and if it is not spam, the program will still classify it as “spam” with probability 0.1.spam, the program will still classify it as “spam” with probability 0....
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