When it comes to experiments involving probability, several core principles dictate the impact of the number of trials on the outcomes. Based on the information that Frederick spun a spinner 20 times and recorded a 4 on five occasions, let's analyze each statement:
1. For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
- True. Increasing the number of trials typically gives a better approximation of the theoretical or predicted probability. This concept is grounded in the Law of Large Numbers, which states that as the number of trials increases, the experimental probability tends to get closer to the theoretical probability.
2. For the experimental outcomes to be closer to the predicted outcome, the number of trials should be decreased.
- False. Decreasing the number of trials will generally lead to a larger variation in results and a greater deviation from the predicted outcomes. A smaller number of trials can result in less reliable data and a higher chance of anomalies.
3. If the number of trials is changed, the experimental probability also changes.
- True. When the number of trials is altered, the experimental probability is likely to change as well. With more trials, there is typically a reduction in the variability of the results, leading the experimental probability to stabilize around the theoretical probability. Conversely, fewer trials can lead to a greater deviation of the experimental probability from the predicted probability due to higher randomness and less averaging out.
To summarize:
- The number of trials should be increased to get experimental outcomes closer to the predicted outcomes.
- Decreasing the number of trials is counterproductive for achieving accuracy.
- Changing the number of trials will indeed alter the experimental probability.
Based on these principles, the true statements are:
- For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
- If the number of trials is changed, the experimental probability also changes.
