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Unformatted text preview: Lecture 9. Some Problems Report on Homework due 02/08/2011 Problem 1. Suppose that 28 crayons, of which 4 are red, are divided randomly among Jack, Marty, Sharon and Martha (seven each). If Sharon has exactly one red crayon, what is the probability that Marty has the remaining 3? (Section 3.1, problem 17) Solution by Yanshan Chen. If Sharon has received seven crayons, including exactly one red one, there are 21 crayons left to distribute, and there are three reds among them. Marty may receive any of the ( 21 7 ) selections, and all are equally likely. To get all three reds in his hand of 7, Marty must receive all of them, as well as 4 of the 18 non-red crayons. There are ( 18 4 ) ways. Thus, his chance of getting the three reds is: ( 18 4 ) ( 21 7 ) = 7 · 6 · 5 21 · 20 · 19 = 1 38 . Problem 2. A child has run away. It is known that she must be in one of three locations, and the probability of being in region i is estimated to be α i . (Note that α 1 + α 2 + α 3 = 1.) It is also estimated that...
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- Spring '08