Question

jamie rolls a 6-sided die 30 times and determines that the experimental probability of rolling a 2 is \\(\frac{1}{15}\\). the theoretical probability of rolling a 2 is \\(\frac{1}{6}\\). what could jamie do to make his experimental results more closely match the theoretical probability? he can increase the number of trials. he can decrease the number of trials. he can increase the number of sides on the die. he can decrease the number of sides on the die.

Explanation:

Step1: Recall Probability Experiment Principles

In probability, as the number of trials (experiments) increases, the experimental probability (from trials) gets closer to the theoretical probability (based on math). Changing the die's sides (options C, D) changes the theoretical probability, not make experimental match original theoretical. Decreasing trials (option B) makes experimental probability less reliable.

Step2: Evaluate Each Option

• Option A: Increasing trials. More trials → experimental prob closer to theoretical (Law of Large Numbers).
• Option B: Decreasing trials. Less data → experimental prob less likely to match theoretical.
• Option C: Increasing die sides. Changes theoretical prob (new die, new theoretical), not match original theoretical.
• Option D: Decreasing die sides. Also changes theoretical prob, not helpful.

Answer:

A. He can increase the number of trials.