Two fair six-sided dice are rolled. What is the probability that the sum of the two numbers rolled is 7?
- A1/12
- B5/36
- C1/6
- D7/36
- E2/9
Two dice: count the favorable outcomes
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: C
Each die is independent, so there are 6 × 6 = 36 equally likely ordered outcomes.
Count the outcomes that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). That is 6 outcomes.
Probability = 6/36 = 1/6.
Two details matter. First, (2,5) and (5,2) are distinct outcomes because the dice are distinct objects (think of one as red, one as blue). If you count only unordered pairs you get 21 outcomes and 3 favorable ones, which gives 3/21, the right answer by the wrong method only because the unordered outcomes are not equally likely (doubles are half as likely as non-doubles), and the ratio happens to survive here.
Second, 7 is the most likely sum precisely because it has the most combinations, 6 of them. Sums of 2 and 12 have only one each. That distribution is worth internalizing: it shows up in probability questions on both exams.
Trap (D), 7/36, counts the number 7 itself as a seventh outcome. Trap (A), 1/12, divides 6 by 72, doubling the sample space.