Two different numbers are chosen at random from 1 to 9. What is the probability that their sum is even?

Explanation

1. 01

   An even sum needs both odd or both even: ${}^{5}C_2 + {}^{4}C_2 = 10 + 6 = 16$ ways.

2. 02

   Out of ${}^{9}C_2 = 36$, so the probability is $\frac{16}{36} = \frac{4}{9}$.