Answer :
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]
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]
