When assessing experimental outcomes in probability, it's important to consider the Law of Large Numbers. This law states that as the number of trials increases, the experimental probability will tend to get closer to the theoretical or predicted probability. This means that with more trials, our experimental results should become more accurate and closer to the expected outcomes.
Let's apply this concept to the given situation:
Frederick spun a spinner 20 times and recorded the outcomes. In those 20 spins, the spinner landed on a 4 five times.
Firstly, let's determine the experimental probability:
- The number of times the spinner landed on 4: 5
- The total number of spins: 20
Experimental Probability (landing on a 4) = Number of times landed on 4 / Total number of spins = 5 / 20 = 1/4 or 0.25 or 25%.
If we want Frederick's experimental outcomes to be closer to the true, or predicted, probability (which is what we typically aim for in probability experiments), we need to increase the number of trials. The larger the sample size (number of trials), the more accurate the experimental probability is likely to be in approximating the theoretical probability.
Thus, the correct statement would be:
- For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
The statement suggesting a decrease in the number of trials is incorrect, as fewer trials typically result in greater variance and less reliable outcomes that may diverge significantly from the expected probability.
Hence, the right answer to the question is:
- For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
