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Unformatted text preview: ORIE 360/560 Fall 2007 Assignment 1 Due Tuesday, Sept. 4 at 2:00 pm Problem 1. A fair coin is tossed 5 times. (a) Write down a description of a reasonable probability space Ω for this problem. How many elements does Ω contain? (b) Find the probability that the first 3 flips are the same. (c) Find the probability that either the first 3 flips are the same, or the last 3 flips are the same, or that both are true. (d) Find the probability that there are at least 2 heads among the first 3 flips and at least 2 tails among the last three flips. (Hint: partition the probability space based on the outcome of the third flip.) Problem 2. A proper basketball team consists of 2 guards, 2 forwards, and 1 center. A certain team has a roster consisting of 6 guards, 4 forwards, and 2 centers. Five people are selected at random from the roster. Find the probability that (a) At least 2 guards will be selected....
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 Spring '10
 SAMORODNITSKY
 Probability, Probability theory, Ordered pair, Elementary mathematics, Probability space

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