Question

If two six-sided similar dice are rolled, then the probability that the sum of the numbers on the two dice is not equal to 7 is:

• A. \( \frac{1}{6} \)
• B. \( \frac{7}{6} \)
• C. \( \frac{5}{6} \)
• D. \( \frac{5}{36} \)

Hint:

To find the probability that the sum is not 7, subtract the probability of getting a sum of 7 from 1.

Answer 1

The Correct Option is C

Let’s break down the solution step by step: Step 1: The total possible outcomes when two dice are rolled is \( 6 \times 6 = 36 \).
The number of favorable outcomes where the sum is 7 (i.e., the pairs (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1)) is 6. Thus, the number of outcomes where the sum is not equal to 7 is \( 36 - 6 = 30 \).
Therefore, the probability is: \[ P(\text{sum is not 7}) = \frac{30}{36} = \frac{5}{6} \]

Step 2: Conclusion:
Since the probability of the sum not being 7 is \( \frac{5}{6} \), the correct answer is (3) \( \frac{5}{6} \).