Question

in a certain town, 45% of the voters support a school referendum up for a vote. sharon will ask people about why they support the referendum, but she needs to find people who support it. what is the probability that it takes 7 people to find the first person who supports the referendum? 0.0125 0.0277 0.0872 0.4500

Explanation:

Step1: Identify the probability of success and failure

The probability of a person supporting the referendum (success) \(p = 0.45\). The probability of a person not supporting the referendum (failure) \(q=1 - p=1 - 0.45 = 0.55\)

Step2: Use the geometric probability formula

The geometric probability formula is \(P(X = k)=q^{k - 1}p\), where \(k\) is the number of trials until the first success. Here \(k = 7\)

Substitute \(q = 0.55\), \(k = 7\) and \(p=0.45\) into the formula:

$$
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$$

Calculate \((0.55)^{6}=0.55\times0.55\times0.55\times0.55\times0.55\times0.55\approx0.0277\)

Then \(P(X = 7)=0.0277\times0.45\approx0.0125\)

Answer:

0.0125