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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]


Sagot :

Sure, let's solve this problem step-by-step.

1. Number of People with Each Eye Color:
- Brown: 20
- Green: 6
- Blue: 17
- Hazel: 7

2. Total Number of People Surveyed:
To find the total number of people surveyed, add the number of people with each eye color:
[tex]\[ 20 \ (\text{brown}) + 6 \ (\text{green}) + 17 \ (\text{blue}) + 7 \ (\text{hazel}) = 50 \][/tex]
So, the total number of people surveyed is 50.

3. Number of People with Brown or Green Eyes:
To find the number of people with either brown or green eyes, add the number of people with brown eyes to the number of people with green eyes:
[tex]\[ 20 \ (\text{brown}) + 6 \ (\text{green}) = 26 \][/tex]

4. Probability that a Person Chosen at Random Has Brown or Green Eyes:
Probability is calculated by dividing the number of favorable outcomes (people with brown or green eyes) by the total number of outcomes (total people surveyed):
[tex]\[ \text{Probability} = \frac{\text{Number of people with brown or green eyes}}{\text{Total number of people surveyed}} = \frac{26}{50} \][/tex]

5. Simplifying the Fraction:
To simplify the fraction [tex]\(\frac{26}{50}\)[/tex], divide the numerator and the denominator by their greatest common divisor (GCD), which is 2:
[tex]\[ \frac{26 \div 2}{50 \div 2} = \frac{13}{25} \][/tex]

Therefore, 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]\[ \boxed{\frac{13}{25}} \][/tex]
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