Discrete Mathematics with Applications 4th Edition

Published by Cengage Learning
ISBN 10: 0-49539-132-8
ISBN 13: 978-0-49539-132-6

Chapter 9 - Counting and Probability - Exercise Set 9.2 - Page 537: 13

Answer

a. In each of the four tosses there are two possible results: Either a head (H) or a tail (T ) is obtained. Thus, by the multiplication rule, the number of outcomes is 2·2·2·2 = 24 = 16. b. There are six outcomes with two heads: HHTT, HTHT, HTTH, THHT, THTH, TTHH. Thus the probability of obtaining exactly two heads is 6/16 = 3/8. c. There are four outcomes with one head: HTTT, THTT, TTHT, TTTH. Thus the probability of obtaining exactly two heads is 4/16 = 1/4.

Work Step by Step

a. In each of the four tosses there are two possible results: Either a head (H) or a tail (T ) is obtained. Thus, by the multiplication rule, the number of outcomes is 2·2·2·2 = 24 = 16. b. There are six outcomes with two heads: HHTT, HTHT, HTTH, THHT, THTH, TTHH. Thus the probability of obtaining exactly two heads is 6/16 = 3/8. c. There are four outcomes with one head: HTTT, THTT, TTHT, TTTH. Thus the probability of obtaining exactly two heads is 4/16 = 1/4.
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