Multiple choice

Two dice are thrown simultaneously. Calculate the probability that their sum is a multiple of either 3 or 4.

  1. 1/6

  2. 1/2

  3. 5/9

  4. 17/36

  5. None of these
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C Correct answer
Explanation

Multiples of 3: 3, 6, 9, 12. Multiples of 4: 4, 8, 12. Combined: 3, 4, 6, 8, 9, 12. Frequencies: 3(2), 4(3), 6(5), 8(5), 9(4), 12(1). Total = 2+3+5+5+4+1 = 20. Probability = 20/36 = 5/9.

AI explanation

When two dice are thrown, the total number of outcomes in the sample space is 6 multiplied by 6, which equals 36. The sums that are multiples of 3 are 3, 6, 9, and 12, accounting for 12 outcomes, while the sums that are multiples of 4 are 4, 8, and 12, accounting for 9 outcomes. Since the sum of 12 is counted in both sets, we use the principle of inclusion-exclusion to find the total favorable outcomes as 12 plus 9 minus the 1 overlapping outcome, which equals 20. The probability is 20 divided by 36, which simplifies to 5/9.

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