Question

the venn diagram on the right shows the results of a gfk roper public affairs and media survey of 1967 american adults taken on october 9, 2012. use the venn diagram to determine whether the following statement is true or false. if the statement is false, make the necessary change to produce a true statement. 60% of those surveyed liked cats or dogs. choose the correct answer below. a. the statement is true. b. the statement is false because 93% of those surveyed liked cats or dogs. c. the statement is false because 33% of those surveyed liked cats or dogs. d. the statement is false because 60% of those surveyed liked cats or dogs.

Explanation:

Step1: Recall formula for union in Venn - diagram

The percentage of people who like cats or dogs is given by \(P(C\cup D)=P(C)+P(D)-P(C\cap D)\). Here, \(P(C) = 4 + 60=64\%\), \(P(D)=29 + 60 = 89\%\), and \(P(C\cap D)=60\%\). So \(P(C\cup D)=(4 + 60)+(29 + 60)-60=93\%\).

Step2: Analyze the given statement

The statement says \(60\%\) of those surveyed liked cats or dogs, which is false. The correct percentage is \(93\%\).

Answer:

B. The statement is false because 93% of those surveyed liked cats or dogs