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.
| Eye Color | Number of People |
|---|---|
| brown | 20 |
| green | 6 |
| blue | 17 |
| hazel | 7 |
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 (2)
Calculate the total number of people: 20 + 6 + 17 + 7 = 50 .
Calculate the number of people with brown or green eyes: 20 + 6 = 26 .
Calculate the probability: 50 26 .
Simplify the fraction: 50 26 = 25 13 .
Explanation
Understand the problem We are given the number of people with each eye color: brown, green, blue, and hazel. We need to find the probability that a randomly chosen person has brown or green eyes.
Calculate the total number of people First, we need to find the total number of people who responded to the survey. We add the number of people with each eye color: 20 ( b ro w n ) + 6 ( g ree n ) + 17 ( b l u e ) + 7 ( ha ze l ) = 50 So, there are a total of 50 people.
Calculate the number of people with brown or green eyes Next, we need to find the number of people with brown or green eyes. We add the number of people with brown eyes and the number of people with green eyes: 20 ( b ro w n ) + 6 ( g ree n ) = 26 So, there are 26 people with brown or green eyes.
Calculate the probability Now, we can find the probability that a randomly chosen person has brown or green eyes. The probability is the number of people with brown or green eyes divided by the total number of people: Total number of people Number of people with brown or green eyes = 50 26 We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2: 50 26 = 50 ÷ 2 26 ÷ 2 = 25 13
State the final answer Therefore, the probability that a person chosen at random from this group has brown or green eyes is 25 13 .
Examples
Imagine you're organizing a school event and want to estimate how many students might need special accommodations based on eye color. Knowing the probability of students having brown or green eyes helps you plan for resources and ensure everyone can participate comfortably. For example, if you know that the probability of a student having brown or green eyes is 25 13 , and you expect 100 students, you can estimate that approximately 25 13 × 100 = 52 students might have brown or green eyes.
The probability that a person chosen at random from the surveyed group has either brown or green eyes is \frac{13}{25}. This was calculated by determining the total number of people surveyed and the number of people with brown or green eyes. The result simplifies to \frac{13}{25}.
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