Multiple choice

Harshad and Amit have thrown two dices. If Harshad has thrown a sum 10 on the two dices, what is Amit`s chance of throwing a sum higher than the sum thrown by the Harshadr?

  1. 1/12

  2. 1/10

  3. ¼

  4. 1/16

  5. 1/8
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A Correct answer
Explanation

Harshad's sum is 10. Possible pairs for 10 are (4,6), (5,5), (6,4) - 3 outcomes. Total outcomes for two dice = 36. Amit needs a sum > 10 (i.e., 11 or 12). Sum 11: (5,6), (6,5) - 2 outcomes. Sum 12: (6,6) - 1 outcome. Total favorable = 3. Probability = 3/36 = 1/12.

AI explanation

Amit needs to throw a sum strictly higher than 10, meaning he must roll a sum of 11 or 12. The combinations that yield a sum of 11 are (5, 6) and (6, 5), while the only combination for 12 is (6, 6), giving exactly 3 favorable outcomes. Since the total number of outcomes when rolling two dice is 36, the probability is 3 divided by 36, which simplifies to 1/12.

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