Probability of Sum of Two Die Rolls

A six-sided die is rolled twice. What is the probability that the sum of the two rolls is equal to 7?

To find the probability, consider all possible outcomes when rolling a die twice. Each die has 6 faces, and thus the total number of outcomes when rolling the die two times is $6 \times 6 = 36$.

Next, identify the combinations that result in a sum of 7: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). There are 6 favorable outcomes.

Using the formula for probability, the probability $P$ of rolling a sum of 7 is given by:

$$P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{6}{36} = \frac{1}{6}.$$