Two dice are thrown simultaneously Find the probability of getting a multiple of 3 as the sum
- $\displaystyle \frac{1}{2}$
- $\displaystyle \frac{1}{3}$
- $\displaystyle \frac{1}{4}$
- $\displaystyle \frac{5}{6}$
Reveal answer
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B
Correct answer
Explanation
Multiples of 3 as sums: 3, 6, 9, 12. Ways: 3 (2 ways), 6 (5 ways), 9 (4 ways), 12 (1 way). Total = 2+5+4+1 = 12. Probability = 12/36 = 1/3.
AI explanation
When two dice are thrown simultaneously, the total number of possible outcomes in the sample space is 6 multiplied by 6, which equals 36. The combinations that yield a sum which is a multiple of 3 are those adding up to 3, 6, 9, and 12; there are 2, 5, 4, and 1 such combinations respectively, for a total of 12 favorable outcomes. By the classical definition of probability, the required probability is the number of favorable outcomes divided by the total outcomes, which is 12/36, simplifying to 1/3.