Two distinct numbers are selected at random from the integers 1 to 20. What is the probability that their product is divisible by 3?

The product is divisible by 3 unless neither number is a multiple of 3.

Multiples of 3 in 1–20: 3, 6, …, 18 → 6 numbers; the other 14 are not.

P(neither is a multiple of 3) = C(14, 2)/C(20, 2) = 91/190.

Required probability = 1 − 91/190 = 99/190.

Trap: 91/190 is the complement; 3/10 is simply the chance a single number is a multiple of 3.