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Chapter 4: Problem 121

Twenty percent of a town's voters favor letting a major discount store move into their neighborhood, \(63 \%\) are against it, and \(17 \%\) are indifferent. What is the probability that a randomly selected voter from this town will either be against it or be indifferent? Explain why this probability is not equal to \(1.0\).

Short Answer

Expert verified
The probability that a randomly selected voter from this town will either be against the store opening or be indifferent is \(0.8\) or \(80 \%\). This probability is not equal to \(1.0\) because not all possible outcomes were considered; in this case, the persons who favor the opening of the store were excluded from the calculation.

Step by step solution

01

Identify the Given Probabilities

From the problem, it is known that the probability that a person is against the store is \(63 \%\), and the probability that a person is indifferent about the store is \(17 \%\). These values should be converted to decimal form for the calculations, which will give \(0.63\) and \(0.17\) respectively.
02

Addition of Probabilities

Since the question asks for the probability that a randomly chosen person is either against or indifferent about the store opening, we need to add these two probabilities. Therefore, we add \(0.63\) and \(0.17\) to get \(0.80\) or \(80 \%\).
03

Explanation for the Probability not being Equal to 1.0

The result is not equal to \(1.0\) or \(100 \%\), because some persons in the town favor the opening of the store. There is a \(20 \%\), or \(0.2\), chance that a randomly selected person will be in favor of the store opening. Therefore, not all possible outcomes were considered in the problem.

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