Multiple choice

Two dice are thrown simultaneously, the probability that the sum of the numbers is divisible by 3 or 4 is _____.

  1. 5/36

  2. 5/18

  3. 5/9

  4. 7/36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total outcomes = 36. Sums divisible by 3: 3, 6, 9, 12 (sums 3, 6, 9, 12 occur 2, 5, 4, 1 times = 12). Sums divisible by 4: 4, 8, 12 (sums 4, 8, 12 occur 3, 5, 1 times = 9). Intersection (divisible by 12): sum 12 (1 time). Total = 12 + 9 - 1 = 20. Probability = 20/36 = 5/9.

AI explanation

When two dice are thrown, there are 36 possible outcomes. The sums divisible by 3 are 3, 6, 9, and 12, giving 12 combinations, while the sums divisible by 4 are 4, 8, and 12, giving 9 combinations. Removing the one duplicate combination for the sum of 12 results in exactly 20 favorable outcomes, making the probability 20/36 or 5/9.

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