Brainteaser - Prime Numbers

Consider the first \( 16 \) prime numbers: \[ \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53\}. \]If we randomly select \( 4 \) of these numbers without replacement, what is the probability that their sum will be even?