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Chapter 7: Problem 31

An opinion poll was conducted among a group of registered voters in a certain state concerning a proposition aimed at limiting state and local taxes. Results of the poll indicated that \(35 \%\) of the voters favored the proposition, \(32 \%\) were against it, and the remaining group were undecided. If the results of the poll are assumed to be representative of the opinions of the state's electorate, what is the probability that a registered voter selected at random from the electorate a. Favors the proposition? b. Is undecided about the proposition?

Short Answer

Expert verified
The probability that a randomly selected voter favors the proposition is \(0.35\), and the probability that a randomly selected voter is undecided about the proposition is \(0.33\).

Step by step solution

01

a. Probability of Favoring the Proposition

To find the probability that a randomly selected voter favors the proposition, we can use the percentage given in the problem. Since \(35 \%\) of the voters favor the proposition, the probability that a randomly selected voter favors the proposition is \(\frac{35}{100}\).
02

a. Result

The probability that a randomly selected voter favors the proposition is \(\frac{35}{100}\) or \(0.35\).
03

b. Probability of Being Undecided About the Proposition

To find the probability that a randomly selected voter is undecided about the proposition, we need the percentage of undecided voters. This can be calculated by taking the total percentage of voters (\(100 \%\)) and subtracting the percentage of voters in favor of the proposition (\(35 \%\)) and the percentage of voters against the proposition (\(32 \%\)). This gives us the percentage of undecided voters: \(100 \% - 35 \% - 32 \% = 33 \%\). Therefore, the probability that a randomly selected voter is undecided about the proposition is \(\frac{33}{100}\).
04

b. Result

The probability that a randomly selected voter is undecided about the proposition is \(\frac{33}{100}\) or \(0.33\).

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