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The people who responded to a survey reported that they had either brown, green, blue, or hazel eyes. The results of the survey are shown in the table.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Eye Color & \begin{tabular}{c}
Number of \\
People
\end{tabular} \\
\hline
brown & 20 \\
\hline
green & 6 \\
\hline
blue & 17 \\
\hline
hazel & 7 \\
\hline
\end{tabular}
\][/tex]

What is the probability that a person chosen at random from this group has brown or green eyes?

A. [tex]$\frac{3}{25}$[/tex]

B. [tex]$\frac{7}{25}$[/tex]

C. [tex]$\frac{13}{25}$[/tex]

D. [tex]$\frac{17}{25}$[/tex]



Answer :

GinnyAnswer
Let's solve this step-by-step.

1. Determine the total number of people surveyed.
We need to add the counts of people with each eye color.
- Brown eyes: 20 people
- Green eyes: 6 people
- Blue eyes: 17 people
- Hazel eyes: 7 people

Total number of people = [tex]\(20 + 6 + 17 + 7 = 50\)[/tex]

2. Calculate the number of people with either brown or green eyes.
- Brown eyes: 20 people
- Green eyes: 6 people

Number of people with brown or green eyes = [tex]\(20 + 6 = 26\)[/tex]

3. Find the probability that a person chosen at random has either brown or green eyes.
Probability is calculated as the number of successful outcomes divided by the total number of possible outcomes.
Probability = [tex]\(\frac{\text{Number of people with brown or green eyes}}{\text{Total number of people}}\)[/tex]
Probability = [tex]\(\frac{26}{50}\)[/tex]

4. Simplify the fraction [tex]\(\frac{26}{50}\)[/tex].
Let's simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2.
[tex]\[ \frac{26}{50} = \frac{26 \div 2}{50 \div 2} = \frac{13}{25} \][/tex]

Thus, the probability that a person chosen at random from this group has brown or green eyes is [tex]\(\frac{13}{25}\)[/tex].

So the correct answer is:
[tex]\[ \frac{13}{25} \][/tex]

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