To find the probability of selecting a student with blue eyes, we first need to determine the total number of students surveyed.
The total number of students is the sum of all students with different eye colors:
\[ 20 , (\text{blue}) + 12 , (\text{brown}) + 10 , (\text{green}) + 8 , (\text{amber}) + 6 , (\text{hazel}) + 4 , (\text{gray}) = 60 \]
Now, the total number of students with blue eyes is 20.
The probability \( P \) of selecting a student with blue eyes is given by the formula:
\[ P(\text{blue}) = \frac{\text{Number of students with blue eyes}}{\text{Total number of students}} = \frac{20}{60} \]
To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 20:
\[ \frac{20 \div 20}{60 \div 20} = \frac{1}{3} \]
Thus, the chance of selecting a student with blue eyes is \(\boxed{\frac{1}{3}}\).