Multiple choice

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is a prime number ?

  1. $\dfrac{5}{12}$
  2. $\dfrac{1}{2}$
  3. $\dfrac{7}{12}$
  4. $\dfrac{2}{3}$
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A Correct answer
Explanation

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

AI explanation

When two dice are thrown, the possible prime sums are 2, 3, 5, 7, and 11, which can occur in 1, 2, 4, 6, and 2 ways respectively. The total number of favorable outcomes is the sum of these, which is 15. Therefore, the required probability is 15 divided by 36, which simplifies to 5 over 12.

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