To determine which number of simulation trials would be most likely to produce results closest to those predicted by probability theory, we can use the Law of Large Numbers. This principle states that as the number of trials in a probability experiment increases, the experimental results will tend to get closer to the expected values predicted by probability theory.
Let's analyze the options given:
A. 50 trials
B. 60 trials
C. 40 trials
D. 30 trials
Here are the steps to determine the best option:
1. Understand the Law of Large Numbers: The Law of Large Numbers implies that the larger the number of trials, the more accurate and consistent the results will be with the theoretical probabilities. This is because random variations tend to average out as more trials are conducted.
2. Compare the Number of Trials: Look at the number of trials for each option:
- Option A: 50 trials
- Option B: 60 trials
- Option C: 40 trials
- Option D: 30 trials
3. Select the Largest Number of Trials: Since the Law of Large Numbers favors a larger number of trials, we should select the option with the highest number of trials to get results that are closest to the theoretical predictions.
Among the options given, 60 trials (Option B) is the highest.
Therefore, the number of simulation trials that would be likely to produce results closest to those predicted by probability theory is:
B. 60
