Question

If a die is rolled twice, what is the probability that the sum of the numbers is 7?

• A. $\frac{5}{36}$
• B. $\frac{1}{12}$
• C. $\frac{1}{36}$
• D. $\frac{1}{6}$

Hint:

For rolling two dice, use the total number of outcomes and favorable outcomes to find probabilities.

Answer 1

The Correct Option is D

The problem involves calculating the probability that the sum of the numbers rolled on two dice is 7. A die has 6 faces, so when rolled twice, there are a total of \(6 \times 6 = 36\) possible outcomes. We need to find the outcomes where the sum is 7.
Consider the pairs \((a, b)\) where \(a\) is the result of the first roll and \(b\) is the result of the second roll. We have:
1. \((1, 6)\)
2. \((2, 5)\)
3. \((3, 4)\)
4. \((4, 3)\)
5. \((5, 2)\)
6. \((6, 1)\)
These are the 6 favorable outcomes where the sum of the two numbers is 7.
Therefore, the probability \(P(S)\) of rolling a sum of 7 is calculated as the number of favorable outcomes divided by the total number of possible outcomes:
\[P(S) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6}\]
Hence, the correct answer is \(\frac{1}{6}\).