Question

A pair of dice is thrown. The probability that the sum is neither 7 nor 8 is

• A. \( \frac{11}{36} \)
• B. \( \frac{15}{36} \)
• C. \( \frac{17}{36} \)
• D. \( \frac{25}{36} \)

Hint:

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.

Answer 1

The Correct Option is D

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. \( \frac{25}{36} \).