What is the probability of rolling a sum of 7 on two six-sided dice?

To determine the probability of rolling a sum of 7 with two six-sided dice, we first need to identify all the possible outcomes when rolling the dice. Each die has 6 faces, which means there are a total of 36 (6 × 6) possible combinations when rolling two dice.

Next, we should count the specific combinations of dice rolls that result in a sum of 7. The possible pairs are:

• (1, 6)

• (2, 5)

• (3, 4)

• (4, 3)

• (5, 2)

• (6, 1)

This gives us a total of 6 combinations that yield a sum of 7.

Now, to find the probability, we take the number of successful outcomes (which is 6) and divide it by the total number of possible outcomes (which is 36). Thus, the probability can be calculated as:

Probability = Number of successful outcomes / Total number of outcomes = 6 / 36 = 1 / 6.

This confirms that the correct answer represents the likelihood of rolling a sum of 7, as there are 6 favorable outcomes out of 36 total possible outcomes.