Parity of a Prime Draw

Take the sixteen smallest primes,{2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53}, \{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53\}, and draw 4 4 of them at random without replacement. What is the probability that the four drawn numbers add up to an even total?

Answer

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