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