Multiple choice

Two unbiased dice are drawn. Find the probability that neither a doublet nor a total of $8$ will appear.

  1. $\dfrac {15}{18}$
  2. $\dfrac {11}{18}$
  3. $\dfrac {13}{15}$
  4. $\dfrac {13}{18}$
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D Correct answer
Explanation

Total outcomes for two dice are 36. Doublets are (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) [6 outcomes]. Sum of 8 outcomes are (2,6), (3,5), (4,4), (5,3), (6,2) [5 outcomes]. Since (4,4) is counted in both, total unique outcomes to exclude are 6 + 5 - 1 = 10. Probability of neither is 1 - (10/36) = 26/36 = 13/18.

AI explanation

When two dice are thrown, the total number of outcomes is 36. There are 6 doublets, and there are 5 outcomes that sum to 8, but (4, 4) is counted in both, giving 10 restricted outcomes. The number of outcomes that are neither doublets nor sum to 8 is 36 minus 10, which is 26. The required probability is 26 divided by 36, which simplifies to 13 divided by 18.

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