Multiple choice

If two standard dice are rolled, what is the probability that the sum of the digits on the two dice is a prime number?

  1. $\dfrac {5}{6}$
  2. $\dfrac {5}{12}$
  3. $\dfrac {5}{26}$
  4. $\dfrac {4}{13}$
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B Correct answer
Explanation

Total outcomes = 36. Sums that are prime: 2 (1,1), 3 (1,2; 2,1), 5 (1,4; 2,3; 3,2; 4,1), 7 (1,6; 2,5; 3,4; 4,3; 5,2; 6,1), 11 (5,6; 6,5). Total prime outcomes = 1+2+4+6+2 = 15. Probability = 15/36 = 5/12.

AI explanation

When two standard dice are rolled, the total number of possible outcomes is 36. The prime number sums possible are 2, 3, 5, 7, and 11. The favorable outcomes for these sums are (1,1), (1,2), (2,1), (1,4), (2,3), (3,2), (4,1), (1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (5,6) and (6,5), totaling 15. Using the classical probability formula, the probability is 15 divided by 36, which simplifies to 5 divided by 12.

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