Multiple choice

In how many ways can two dice be rolled, so that the sum of the values on the upper faces is divisible by three?

  1. 9

  2. 12

  3. 15

  4. 18
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 36 total outcomes when rolling two dice. The sums divisible by 3 are 3, 6, 9, and 12. The pairs summing to 3 are (1,2), (2,1); to 6 are (1,5), (2,4), (3,3), (4,2), (5,1); to 9 are (3,6), (4,5), (5,4), (6,3); and to 12 is (6,6). Counting these gives 2 + 5 + 4 + 1 = 12 outcomes.

AI explanation

When two dice are rolled, the total number of possible outcomes in the sample space is 36. The favorable sums divisible by 3 are 3, 6, 9 and 12, which occur in 2, 5, 4 and 1 ways respectively. Adding these favorable outcomes gives 2 plus 5 plus 4 plus 1 equals 12, so the required number of ways is 12.

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