Question:
A pair of dice is thrown. The probability that the sum is neither 7 nor 8 is
A pair of dice is thrown. The probability that the sum is neither 7 nor 8 is
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When calculating probabilities involving dice rolls, count the outcomes for the desired sums, then subtract from the total number of possible outcomes to find the complementary probability.
Updated On: May 4, 2025
- \( \frac{11}{36} \)
- \( \frac{15}{36} \)
- \( \frac{17}{36} \)
- \( \frac{25}{36} \)
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The Correct Option is D
Solution and Explanation
When two dice are thrown, there are a total of \( 6 \times 6 = 36 \) possible outcomes.
- The sum of 7 can be obtained in the following combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) — 6 outcomes.
- The sum of 8 can be obtained in the following combinations: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) — 5 outcomes.
Thus, the total number of outcomes where the sum is 7 or 8 is \( 6 + 5 = 11 \). The probability that the sum is neither 7 nor 8 is: \[ \frac{36 - 11}{36} = \frac{25}{36} \]
Therefore, the correct answer is 4. \( \frac{25}{36} \).
- The sum of 7 can be obtained in the following combinations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) — 6 outcomes.
- The sum of 8 can be obtained in the following combinations: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2) — 5 outcomes.
Thus, the total number of outcomes where the sum is 7 or 8 is \( 6 + 5 = 11 \). The probability that the sum is neither 7 nor 8 is: \[ \frac{36 - 11}{36} = \frac{25}{36} \]
Therefore, the correct answer is 4. \( \frac{25}{36} \).
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