Multiple choice

A pair of dice is rolled and the numbers appearing on them have a sum greater than or equal to 10. The probability of getting the sum 10 is

  1. 1/6

  2. 1/4

  3. 1/3

  4. 1/2

  5. 2/3
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D Correct answer
Explanation

The outcomes with sum >= 10 are (4,6), (5,5), (6,4), (5,6), (6,5), (6,6). There are 6 such outcomes. The outcomes with sum = 10 are (4,6), (5,5), (6,4). The probability of sum 10 given sum >= 10 is 3/6 = 1/2.

AI explanation

We use the conditional probability formula, dividing the probability of a sum of 10 by the probability of a sum greater than or equal to 10. The combinations that sum to at least 10 are (4,6), (5,5), (6,4), (5,6), (6,5) and (6,6), giving 6 total outcomes. The combinations that sum to exactly 10 are (4,6), (5,5) and (6,4), giving 3 outcomes. The conditional probability is 3 divided by 6, which equals 1/2.

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