Multiple choice

Two fair dice are thrown, find the probability that sum of the points on their uppermost faces is greater than $10$ or an odd number:

  1. $\displaystyle \frac{16}{36}$
  2. $\displaystyle \frac{17}{36}$
  3. $\displaystyle \frac{18}{36}$
  4. $\displaystyle \frac{19}{36}$
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D Correct answer
Explanation

The sum is greater than 10 if it is 11 or 12, which occurs in 3 outcomes (5,6), (6,5), (6,6). The sum is odd if it is 3, 5, 7, 9, or 11, which occurs in 18 outcomes. Using the inclusion-exclusion principle, the total favorable outcomes are 3 + 18 - 1 (since 11 is counted in both) = 20, but the question asks for the union of these sets. The sum > 10 is {11, 12} and odd sums are {3, 5, 7, 9, 11}. The union is {3, 5, 7, 9, 11, 12}, which covers 18 + 1 = 19 outcomes.

AI explanation

The total number of outcomes when rolling two dice is 36. The number of outcomes with an odd sum is 18, and the outcomes with a sum greater than 10 are three: (5,6), (6,5), and (6,6). Since these two events are mutually exclusive, we add their individual probabilities: 18/36 plus 3/36. This yields a total probability of 21/36.

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