Precalculus
Precalculus
9th Edition
ISBN: 9780321716835
Author: Michael Sullivan
Publisher: Addison Wesley
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Chapter 13.1, Problem 29AYU

Analyzing Survey Data In a survey of 100 investors in the stock market,

50 owned shares in IBM

40 owned shares in AT&T

45 owned shares in GE

20 owned shares in both IBM and GE

15 owned shares in both AT&T and GE

20 owned shares in both IBM and AT&T

a. How many of the investors surveyed did not have shares in any of the three companies?

b. How many owned just IBM shares?

c. How many owned just GE shares?

d. I low many owned neither IBM nor GE?

e. I low many owned either IBM or AT&T but no GE?

Expert Solution & Answer
Check Mark
To determine

To find:

a. How many of the investors surveyed did not have shares in any of the three companies?

b. How many owned just IBM shares?

c. How many owned just GE shares?

d. How many owned neither IBM nor GE?

e. How many owned either IBM or AT&T but no GE?

Answer to Problem 29AYU

a. 15.

b. 15.

c. 15.

d. 25.

e. 40.

Explanation of Solution

Given:

In a survey of 100 investors in the stock market, 50 owned shares in IBM.

40 owned shares in AT&T.

45 owned shares in GE.

20 owned shares in both IBM and GE.

15 owned shares in both AT&T and GE.

20 owned shares in both IBM and AT&T.

5 owned shares in all three.

Formula used:

n( A  B ) = n( A ) + n( B )  n( A  B )

n() = n( A  B ) + n( A  B ¯ )

Calculation:

From the given data, we draw the venn diagram as shown below.

n( IBM ) = 50

n( AT & T ) = 40

n( GE ) = 45

n( IBM  GE ) = 20

n( AT & T  GE ) = 15

n( IBM  AT & T ) = 20

n( IBM  AT & T  GE ) = 5

n( ( IBM  GE ) only ) = 20  5 = 15

n( ( IBM  AT & T ) only ) = 20  5 = 15

n( ( AT & T  GE ) only ) = 15  5 = 10

n( IBM only ) = 50  15  15  5 = 15

n( AT & T only ) = 40  15  10  5 = 10

n( GE only ) = 45  10  15  5 = 15

Precalculus, Chapter 13.1, Problem 29AYU

From the venn diagram,

a. Number of the investors surveyed did not have shares in any of the three companies is 15.

b. Number of investors who owned just IBM shares are 15.

c. Number of investors who owned just GE shares are 15.

d. Number of investors who owned neither IBM nor GE is n( U ) + n( AT & T only ) = 15 + 10 = 25 .

e. Number of investors who owned either IBM or AT&T but no GE is n( IBM only ) + n( AT & T only ) + n( IBM and AT & T ) = 15 + 15 + 10 = 40 .

Chapter 13 Solutions

Precalculus

Ch. 13.1 - If n( A )=15 , n( B )=20 , and n( AB )=10 , find...Ch. 13.1 - If n( A )=30 , n( B )=40 , and n( AB )=45 , find...Ch. 13.1 - If n( AB )=50 , n( AB )=10 , and n( B )=20 , find...Ch. 13.1 - If n( AB )=60 , n( AB )=40 , and n( A )=n( B ) ,...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - In Problems 15-22, use ihe information given in...Ch. 13.1 - A man has shirts and ties. 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(p. 642)Ch. 13.2 - Prob. 2AYUCh. 13.2 - A(n) __________ is an ordered arrangement of r...Ch. 13.2 - A(n) ___________ is an arrangement of r objects...Ch. 13.2 - P( n,r )= __________________.Ch. 13.2 - C( n,r )= _______________________.Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 7-14, find the value of each...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - In Problems 15-22, use formula (2) to find the...Ch. 13.2 - 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Forming Codes How many different four-letter codes...Ch. 13.2 - Stocks on the NYSE Companies whose stocks are...Ch. 13.2 - Stocks on the NASDAQ Companies whose stocks are...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Establishing Committees In how many ways can a...Ch. 13.2 - Possible Answers on a True/False Test How many...Ch. 13.2 - Possible Answers on a Multiple-choice Test How...Ch. 13.2 - Arranging Books Five different mathematics books...Ch. 13.2 - Prob. 46AYUCh. 13.2 - Birthday Problem In how many ways can 2 people...Ch. 13.2 - Prob. 48AYUCh. 13.2 - Prob. 49AYUCh. 13.2 - Prob. 50AYUCh. 13.2 - Forming Words How many different 9-letter words...Ch. 13.2 - Prob. 52AYUCh. 13.2 - Selecting Objects An urn contains 7 white balls...Ch. 13.2 - Prob. 54AYUCh. 13.2 - Prob. 55AYUCh. 13.2 - Prob. 56AYUCh. 13.2 - Prob. 57AYUCh. 13.2 - Prob. 58AYUCh. 13.2 - Prob. 59AYUCh. 13.2 - Prob. 60AYUCh. 13.2 - Prob. 61AYUCh. 13.2 - Prob. 62AYUCh. 13.2 - Combination Locks A combination lock displays 50...Ch. 13.2 - Prob. 64AYUCh. 13.2 - Prob. 65AYUCh. 13.2 - Prob. 66AYUCh. 13.3 - When the same probability is assigned to each...Ch. 13.3 - Prob. 2AYUCh. 13.3 - Prob. 3AYUCh. 13.3 - Prob. 4AYUCh. 13.3 - In a probability model, which of the following...Ch. 13.3 - Prob. 6AYUCh. 13.3 - Determine whether the following is a probability...Ch. 13.3 - Prob. 8AYUCh. 13.3 - Prob. 9AYUCh. 13.3 - Prob. 10AYUCh. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - Prob. 14AYUCh. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 11-16, construct a probability model...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - In Problems 17-22, use the following spinners to...Ch. 13.3 - 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Prob. 9CTCh. 13 - Prob. 10CTCh. 13 - On February 20, 2004, the Ohio Bureau of Motor...Ch. 13 - Kiersten applies for admission to the University...Ch. 13 - A cooler contains 8 bottles of Pepsi, 5 bottles of...Ch. 13 - Prob. 14CTCh. 13 - Prob. 15CTCh. 13 - Prob. 16CTCh. 13 - Prob. 1CRCh. 13 - Prob. 2CRCh. 13 - Prob. 3CRCh. 13 - Prob. 4CRCh. 13 - Prob. 5CRCh. 13 - Prob. 6CRCh. 13 - Prob. 7CRCh. 13 - Prob. 8CRCh. 13 - Prob. 9CRCh. 13 - Prob. 10CRCh. 13 - Graph: y=3sin(2x+)Ch. 13 - Prob. 12CR

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