A white die and a black die, both fair, are rolled. What is the probability that the number on the black die is a multiple of the number on the white die?

Sort the favourable pairs by the white number w. w = 1 allows all 6 black numbers; w = 2 allows 2, 4, 6 (3 ways); w = 3 allows 3 and 6 (2 ways); and w = 4, 5, 6 each allow only the matching number (1 way each). That is 6 + 3 + 2 + 1 + 1 + 1 = 14 of the 36 outcomes, so the probability is 14/36 = 7/18. Forgetting that every number is a multiple of itself leaves only the strict multiples, 5 + 2 + 1 = 8, giving 2/9; keeping just the w = 1 row and the six equal pairs, which share the outcome (1,1), gives 11/36; and 1/6 counts the equal pairs alone.