What can Tim say about the difference between his experimental probability and the theoretical probability of rolling a sum of 4?

To understand why the answer indicating that the experimental probability is about 4% greater is appropriate, we first need to clarify the concepts of theoretical probability and experimental probability.

Theoretical probability is calculated based on all possible outcomes in a given situation. For rolling two six-sided dice, the total number of possible outcomes is 36 (6 faces on the first die multiplied by 6 faces on the second die). The combinations that yield a sum of 4 are as follows: (1,3), (2,2), and (3,1), totaling 3 favorable outcomes. Therefore, the theoretical probability of rolling a sum of 4 is 3 out of 36, which simplifies to 1/12, or approximately 8.33%.

Experimental probability, on the other hand, is based on actual experiments or trials conducted. If Tim rolls the dice several times and records the outcomes, he could find that the frequency of rolling a sum of 4 is higher due to random variations in his individual trials.

If Tim's experimental probability is determined to be higher than 8.33% by about 4%, then he would conclude that the experimental probability is approximately 12.33%. This kind of discrepancy can happen because experimental results can