Probability 4

The sum of two number is even if they're both even or both odd.

There are 11 even numbers out of the first 23: $\{2, 4, ..., 22\}$

There are 12 odd numbers out of the first 23: $\{1,3,...,23\}$

"Pick two even numbers" and "pick two odd numbers" are incompatible events, therefore the probability is:

$p=\frac{\binom{11}{2}}{\binom{23}{2}}+ \frac{\binom{12}{2}}{\binom{23}{2}}=\boxed{\frac{11}{23}}$