Final answer:
The theoretical probability of rolling a sum of 7 with a pair of number cubes is 1/6. Brett's experimental probability is 1/3, and the difference between the experimental probability and the theoretical probability is 0.
Step-by-step explanation:
The theoretical probability of rolling a sum of 7 with a pair of number cubes is 1/6. This is because there are 6 possible outcomes when rolling a pair of number cubes (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,1), (3,2), (3,3), (3,4), (3,5), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6), and out of those 6 pairs, only 1 has a sum of 7 (1,6) or (6,1). So the probability of rolling a sum of 7 is 1/6.
To find the experimental probability, we take the number of times the event occurred (in this case, rolling a sum of 7) and divide it by the total number of trials (36). In Brett's case, he rolled a sum of 7 for 12 out of 36 rolls. So the experimental probability is 12/36, which simplifies to 1/3.
To find the difference between Brett's experimental probability and the theoretical probability, we subtract the theoretical probability from the experimental probability:
1/3 - 1/6 = 1/3 - 2/6 = 2/6 - 2/6 = 0/6 = 0.
Therefore, the difference between Brett's experimental probability and the theoretical probability is 0.