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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.

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

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 the problem step-by-step to determine the probability that a randomly chosen person from a group has either brown or green eyes.

1. Identify the number of people with each eye color:
- Brown eyes: 20 people
- Green eyes: 6 people
- Blue eyes: 17 people
- Hazel eyes: 7 people

2. Calculate the total number of people surveyed:
[tex]\[ \text{Total number of people} = 20 + 6 + 17 + 7 = 50 \][/tex]

3. Calculate the number of people with brown or green eyes:
- Number of people with brown eyes: 20
- Number of people with green eyes: 6

[tex]\[ \text{Number of people with brown or green eyes} = 20 + 6 = 26 \][/tex]

4. Calculate the probability that a person chosen at random has brown or green eyes:
[tex]\[ \text{Probability} = \frac{\text{Number of people with brown or green eyes}}{\text{Total number of people}} = \frac{26}{50} \][/tex]

5. Simplify the fraction:
[tex]\[ \frac{26}{50} = \frac{13}{25} \][/tex]

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

The correct answer is [tex]\(\boxed{\frac{13}{25}}\)[/tex].

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