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 sides on the die.
he can increase the number of trials.
he can decrease the number of sides on the die.
he can decrease the number of trials.

Explanation:

Step1: Understand the relationship between experimental and theoretical probability

Experimental probability is based on actual trials. Theoretical probability is calculated based on the nature of the event (e.g., for a fair 6 - sided die, \(P(\text{rolling a }2)=\frac{1}{6}\)). As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.

Step2: Analyze each option

• If he increases the number of sides on the die, it changes the theoretical probability, which is not relevant to making the experimental probability match the original theoretical probability (\(\frac{1}{6}\)).
• If he increases the number of trials, by the law of large numbers, the experimental probability \(P_{exp}=\frac{\text{number of times }2\text{ is rolled}}{\text{total number of trials}}\) will approach the theoretical probability \(P_{theo}=\frac{1}{6}\).
• If he decreases the number of sides on the die, it changes the theoretical probability.
• If he decreases the number of trials, the experimental probability is more likely to deviate from the theoretical probability due to less data.

Answer:

He can increase the number of trials.