Question

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Problem Solving Using Theoretical Probabilities Practice
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Question
Use the table to answer the question.

Favorite Color Number of Students
blue 97
green 84
red 43
yellow 26
What is the probability of randomly choosing a student whose favorite color is green? Write your answer as a fraction in the simplest form.

(1 point)

Answer 1

To find the probability of randomly choosing a student whose favorite color is green, we first need to calculate the total number of students surveyed.

We have the following number of students for each color:
- Blue: 97
- Green: 84
- Red: 43
- Yellow: 26

Now, we can calculate the total number of students:

\[
\text{Total} = 97 + 84 + 43 + 26 = 250
\]

Next, the probability of choosing a student whose favorite color is green is given by the formula:

\[
P(\text{Green}) = \frac{\text{Number of students who like green}}{\text{Total number of students}} = \frac{84}{250}
\]

Now, we simplify the fraction \(\frac{84}{250}\).

To simplify, we find the greatest common divisor (GCD) of 84 and 250. The GCD is 2.

Now divide both the numerator and the denominator by the GCD:

\[
\frac{84 \div 2}{250 \div 2} = \frac{42}{125}
\]

Thus, the probability of randomly choosing a student whose favorite color is green is:

\(\frac{42}{125}\)