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]
