A red die and a blue die, both fair, are rolled together. What is the probability that the number on the red die is greater than the number on the blue die?

Of the 36 outcomes, 6 are ties (1-1, 2-2, …, 6-6). The other 30 split evenly between 'red bigger' and 'blue bigger', because swapping the two dice pairs them off, so 15 are favourable and the probability is 15/36 = 5/12. Answering 1/2 forgets that the dice can tie; 7/12 = 21/36 answers 'red is greater than OR EQUAL TO blue'; and 1/6 is the probability of a tie.