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Chapter 4: Problem 80

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 it or be indifferent to the move of a major discount store into their neighborhood is \(0.80\). This probability is not equal to \(1.0\) because the total probability should include all possibilities, including those voters who are in favor of the move, which are \(20\%\) of the total voters.

Step by step solution

01

Identify the data

We know that \(20\%\) of the voters favor letting the discount store move into their neighborhood, \(63\%\) are against it and \(17\%\) are indifferent. We want to find the probability that a randomly selected voter will either be against it or be indifferent.
02

Convert the percentages into probabilities

In probability, ratios, fractions and percentages are often interchangeable. Here, the percentages can be understood directly as probabilities because they represent the respective fraction of the whole community. Hence, the probability that a voter would oppose is \(0.63\) and the probability of them being indifferent is \(0.17\)
03

Compute the combined probability

The probability of a voter being either against or indifferent is equal to the sum of the individual probabilities of each event happening. Therefore, \(0.63 + 0.17 = 0.80\) is the combined probability.
04

Explain why probability does not add up to 1

The sum of probabilities in a complete set of outcomes should add up to 1. However, our computation only includes those who are against or indifferent to the idea. To totalize 1, we would need to add those who are in favor of the store moving in, which in this case is \(0.20\). Hence, \(0.80 + 0.20 = 1.0\).

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