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Unformatted text preview: SPRING 2009 MATH 425 Ralf Spatzier Homework 1 - Solutions (1) If two balanced dice are rolled, what is the probability that the sum of spots is equal to five? Describe the sample space and the event as a subset of the sample space. Solution: The sample space is pairs of integers between 1 and 6. There are 36 of them. 4 of these pairs add up to 6. Hence the probability is 4/36 or 1/9. (2) In how many ways can 11 one dollar coins be divided amongst 7 children? What if each child gets at least one coin? Solution: This corresponds to the problem of writing 11 as the sum of 7 nonnegative integers: 11 = 7 i =1 x i . By Proposition 6.2 form the book, there are ( 17 6 ) many solutions. If every child gets at least one coin, there are ( 10 6 ) many solutions. (3) A drawer contains 4 pairs of socks, one red, one black, one white and one green. If 4 socks are selected at random, what is the probability that the 4 socks include at least one pair?...
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