Question

frederick designed an experiment in which he spun a spinner 20 times and recorded the results of each spin. he spun a 4 five times. which statements are true? choose all that apply.

• for the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.
• for the experimental outcomes to be closer to the predicted outcome, the number of trials should be decreased.
• if the number of trials is changed, the experimental probability also changes.

Explanation:

1. Law of Large Numbers: As the number of trials (spins) increases, experimental probabilities (frequencies of each spin result) tend to approach the theoretical (predicted) probability. So, more trials make outcomes closer to predictions.
2. Regarding "decreased trials": Fewer trials mean more variability (randomness), so outcomes are less likely to match predictions.
3. Regarding "probability changes with trials": Theoretical probability (e.g., chance of spinning a 4) is fixed (here, \( \frac{1}{10} \) for each number). Experimental probability may fluctuate, but the theoretical probability does not change with the number of trials. Thus, this statement is false.

Answer:

The true statements are:

• For the experimental outcomes to be closer to the predicted outcome, the number of trials should be increased.