Discrete Mathematics and Its Applications, Seventh Edition

Published by McGraw-Hill Education
ISBN 10: 0073383090
ISBN 13: 978-0-07338-309-5

Chapter 7 - Section 7.1 - An Introduction to Discrete Probability - Exercises - Page 451: 33

Answer

a) $\frac{1}{7880400}$ b) $\frac{1}{8000000}$

Work Step by Step

a) The probability that Abby takes the first place is 1/200. After Abby, the probability that Barry is second is 1/199. As the 1st place is already taken by Abby. The probability that Sylvia takes the third place is 1/198. As the 1st and 2nd places are already occupied. Hence the Probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively is $1/200 \times 1/199 \times 1/198 $ =$\frac{1}{7880400}$ b)If one person is allowed more than one prize then the probability of 2nd and third changes to 1/200 for both. Hence the Probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively is $1/200 \times 1/200 \times 1/200 $ =$\frac{1}{8000000}$
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