The best prediction for the number of times that Jeremy will roll a number greater than 4 can be determined using probability.
1. **Probability of rolling a number greater than 4 on a fair 6-sided dice:**
- Numbers greater than 4 on a 6-sided dice are 5 and 6.
- So, there are 2 favorable outcomes out of 6 possible outcomes.
- Therefore, the probability of rolling a number greater than 4 = Number of favorable outcomes / Total number of outcomes = 2/6 = 1/3.
2. **Calculating the expected number of times Jeremy will roll a number greater than 4:**
- Expected value = Probability of success * Total number of trials
- Expected number of times Jeremy will roll a number greater than 4 = (1/3) * 180 = 60.
3. **Selecting the best prediction based on the calculation:**
- The best prediction for the number of times that Jeremy will roll a number greater than 4 is **C. exactly 60 times**.
Therefore, the best prediction based on probability theory is that Jeremy will roll a number greater than 4 exactly 60 times out of 180 rolls.
