(a) To determine The total number of people surveyed. Explanation Given: A marine biologist surveys people who fish on Lake Eerie and caught at least one fish to determine whether they had caught a walleye, a smallmouth bass, or a yellow perch in the last year. The data recorded in the survey are given below. 124 caught at least one walleye. 133 caught at least one smallmouth bass. 146 caught at least one yellow perch. 75 caught at least one walleye and at least one smallmouth bass. 67 caught at least one walleye and at least one yellow perch. 79 caught at least one smallmouth bass and at least one yellow perch. 45 caught all three. Explanation: Consider three sets W , S , Y , where W represents the people who caught at least one walleye, S represents the people who caught at least one smallmouth bass and Y represents the people who caught at least one yellow perch. A Venn diagram representing the relationship between the three sets is given below where the parentheses denotes the various regions of the Venn diagram. 45 caught all three fishes. Place 45 in region 5 of the above Venn diagram. Of the 75 people who caught at least walleye and at least one smallmouth bass, 45 also caught yellow perch. Therefore, 75 − 45 = 30 people caught only walleye and smallmouth bass. Place 30 in region 2 of the Venn diagram. Of the 67 people who caught at least walleye and at least one yellow perch, 45 also caught smallmouth bass. Therefore, 67 − 45 = 22 people caught only walleye and yellow perch. Place 22 in region 4 of the Venn diagram. Of the 79 people who caught at least one yellow perch and at least one smallmouth bass, 45 also caught walleye. Therefore, 79 − 45 = 34 people caught only yellow perch and smallmouth bass (b) To determine The total number of people who caught at least one walleye or at least one smallmouth bass. (c) To determine The total number of people who caught only walleye.

Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

11th Edition

ISBN: 9780321931078

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Question

Chapter 8.2, Problem 21E

(a)

To determine

The total number of people surveyed.

(b)

To determine

The total number of people who caught at least one walleye or at least one smallmouth bass.

(c)

To determine

The total number of people who caught only walleye.

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Chapter 8.2, Problem 20E

Chapter 8.2, Problem 22E

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Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)

Ch. 8.1 - Checkpoint 1 Indicate whether each statement is...Ch. 8.1 - Prob. 2CP Ch. 8.1 - Prob. 3CP Ch. 8.1 - Prob. 4CP Ch. 8.1 - Checkpoint 5 Find the number of subsets for each...Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 8.1 - Prob. 8CP Ch. 8.1 - Prob. 9CP Ch. 8.1 - Prob. 10CP

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