Two fair dice are rolled. What is the probability that the sum is 7?

Two fair dice are rolled. What is the probability that the sum is 7?

• A. 5/36
• B. 1/3
• C. 1/9
• D. 1/6

Answer: (D)

To get a sum of seven when rolling two fair dice, count favorable outcomes over total outcomes. There are 36 equally likely results from two dice. The pairs that sum to seven are exactly six: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So the probability is 6/36, which reduces to 1/6. The other numbers would imply different counts of favorable pairs—for example, five favorable pairs would give 5/36, twelve would give 1/3, and four would give 1/9—so they don’t match the actual six ways to total seven.

To get a sum of seven when rolling two fair dice, count favorable outcomes over total outcomes. There are 36 equally likely results from two dice. The pairs that sum to seven are exactly six: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). So the probability is 6/36, which reduces to 1/6.

The other numbers would imply different counts of favorable pairs—for example, five favorable pairs would give 5/36, twelve would give 1/3, and four would give 1/9—so they don’t match the actual six ways to total seven.