To find the probability of selecting a student with blue eyes, you can use the formula for probability:
\[ P(\text{event}) = \frac{\text{number of favorable outcomes}}{\text{total number of outcomes}} \]
From the survey results, the number of students with blue eyes is 20.
Now, we need to calculate the total number of students surveyed by adding up all the students with each eye color:
\[ 20 , (\text{blue}) + 12 , (\text{brown}) + 10 , (\text{green}) + 8 , (\text{amber}) + 6 , (\text{hazel}) + 4 , (\text{gray}) = 60 \]
Now we can use the formula to find the probability of selecting a student with blue eyes:
\[ P(\text{blue eyes}) = \frac{20}{60} \]
To simplify the fraction, divide both the numerator and denominator by their greatest common divisor (GCD), which is 20:
\[ \frac{20 \div 20}{60 \div 20} = \frac{1}{3} \]
Therefore, the probability of selecting a student with blue eyes is:
\[ \boxed{\frac{1}{3}} \]