Question

Two dice are rolled simultaneously. What is the probability that the sum of the numbers on the two dice is at least 10?

• A. \(\frac{1}{6}\)
• B. \(\frac{1}{9}\)
• C. \(\frac{1}{12}\)
• D. \(\frac{1}{18}\)

Hint:

Tip: List all possible outcomes or use systematic counting to avoid missing any cases.

Answer 1

The Correct Option is A

The probability of rolling a sum of at least 10 with two dice is calculated as follows. The total number of possible outcomes when rolling two dice is \(6 \times 6 = 36\), as each die has 6 faces.

The outcomes resulting in a sum of at least 10 are:

• Sum of 10: (4,6), (5,5), (6,4)
• Sum of 11: (5,6), (6,5)
• Sum of 12: (6,6)

There are 6 such favorable outcomes. The probability is the ratio of favorable outcomes to the total possible outcomes:

\(\frac{6}{36} = \frac{1}{6}\)

Consequently, the probability that the sum of the numbers on two dice is at least 10 is \(\frac{1}{6}\).