Two primes with an even sum

Two distinct prime numbers between 11 and 2020 (inclusive) are chosen uniformly at random. What is the probability that their sum is even?

Show hints (2)+
  1. The sum is even iff both primes are odd. Which prime in [1,20][1,20] is the only even one?
  2. Count all-odd pairs (72)\binom{7}{2} over all pairs (82)\binom{8}{2}.

Answer

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0.75

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