Two primes with an even sum

Two distinct prime numbers between $1$ and $20$ (inclusive) are chosen uniformly at random. What is the probability that their sum is even?

Show hints (2)+

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

Answer

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0.75

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