Multiple choice

If two dice are thrown simultaneously, then the probability of getting a doublet or a total of $6$ is

  1. $\dfrac{1}{3}$
  2. $\dfrac{5}{18}$
  3. $\dfrac{7}{18}$
  4. $\dfrac{11}{36}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total outcomes = 36. Doublets: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) [6 outcomes]. Total of 6: (1,5), (2,4), (3,3), (4,2), (5,1) [5 outcomes]. Overlap: (3,3) [1 outcome]. Total favorable = 6 + 5 - 1 = 10. Probability = 10/36 = 5/18.

AI explanation

When two dice are thrown, there are 36 possible outcomes. The number of doublets, where both dice show the same number, is 6, and the number of outcomes totaling exactly 6 is 5: (1, 5), (5, 1), (2, 4), (4, 2), and (3, 3). By the addition rule of probability, we add the doublets and the sums of 6, then subtract the one overlapping outcome of (3, 3), resulting in 6 plus 5 minus 1 equals 10 favorable outcomes. The probability is therefore 10 divided by 36, which simplifies to 5/18.

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