Multiple choice

What is the probability that the sum of two number on two rolled dices will yield a $10$ or lower ?

  1. $\dfrac{1}{4}$.
  2. $\dfrac{7}{12}$.
  3. $\dfrac{5}{12}$.
  4. $\dfrac{11}{12}$.
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D Correct answer
Explanation

The total outcomes when rolling two dice is 36. The outcomes that sum to 11 or 12 are (5,6), (6,5), and (6,6), which are 3 outcomes. The probability of getting 11 or 12 is 3/36 = 1/12, so the probability of getting 10 or lower is 1 - 1/12 = 11/12.

AI explanation

The only way to get a sum greater than 10 when rolling two dice is rolling a (5, 6), (6, 5), or (6, 6), which gives 3 total outcomes. Since the total number of possible outcomes is 36, the probability of rolling a sum greater than 10 is 3 divided by 36, which simplifies to 1/12. The probability of the sum being 10 or lower is the complement, calculated as 1 minus 1/12, resulting in 11/12.

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