Question

In his class, Dale conducted a survey to observe the distribution of eye color. The results are summarized as follows:

This table displays the results from the survey conducted to observe the number of students with different eye colors.
Eye Color Number of Students
blue 20
brown 12
green 10
amber 8
hazel 6
gray 4


If a student is randomly chosen from this group, what is the chance of selecting a student with blue eyes? Write your answer in the simplest form of a fraction.

Answer 1

To find the probability of selecting a student with blue eyes, we first need to determine the total number of students surveyed. We can do this by adding the number of students for each eye color:

- Blue: 20
- Brown: 12
- Green: 10
- Amber: 8
- Hazel: 6
- Gray: 4

Now, let's calculate the total:

\[
20 + 12 + 10 + 8 + 6 + 4 = 70
\]

There are a total of 70 students surveyed.

Next, the number of students with blue eyes is 20. The probability \( P \) of selecting a student with blue eyes can be calculated using the formula:

\[
P(\text{Blue}) = \frac{\text{Number of students with blue eyes}}{\text{Total number of students}} = \frac{20}{70}
\]

Now, we can simplify the fraction \( \frac{20}{70} \):

\[
\frac{20 \div 10}{70 \div 10} = \frac{2}{7}
\]

Thus, the probability of randomly selecting a student with blue eyes is:

\[
\boxed{\frac{2}{7}}
\]