NBCT Mathematics Adolescence And Young Adulthood (AYA) Component 1 Practice Test

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

1/8 1/9 1/6 1/12

Correct Answer:

1/6

Explanation:

Count the outcomes and use probability as favorable outcomes divided by total outcomes. When rolling two fair six-sided dice, there are 6 × 6 = 36 equally likely ordered outcomes. The combinations that sum to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1) — six favorable cases. So the probability is 6 out of 36, which simplifies to 1/6. This matches the intuitive idea that there are six ways to reach 7, out of 36 equally likely possibilities. The other fractions would require a different number of favorable outcomes (for example, four or three), which doesn’t align with the actual six ways to make 7.

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