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hw3-solns - Illinois Institute of Technology Department of...

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Illinois Institute of Technology Department of Computer Science Solutions to Homework Assignment 3 CS 330 Discrete Structures Spring Semester, 2008 1. Page 415, Problem 18. (a) What is the probability that two people chosen at random were born on the same day of the week? Select any one day as the birthday of the first person. It follows that the probability that the second person has the same birthday as the first person is 1/7. (b) What is the probability that a group of n people chosen at random, there are at least two born on the same day? The probability that all birthdays are different is p n = 6 7 × 5 7 × 4 7 × . . . × 8 - n 7 . Since each person after the first must have a different birthday-of-the-week from all previous people in the group. If n 8, p n = 0 since the seventh fraction is 0 (Pigeon Hole Principle). The probability that at least 2 people are born on the same day of the week is therefore 1 - p n . (c) How many people chosen at random are needed to make the probability greater than 1 2 that there are at least 2 people born in the same month of the year?
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