Certainly! Let's explore what Jamie can do to help his experimental probability match the theoretical probability more closely.
### Step-by-Step Solution:
1. Understand the Problem:
- Jamie rolls a 6-sided die 30 times.
- Experimental Probability of rolling a 2: [tex]\( \frac{1}{15} \)[/tex].
- Theoretical Probability of rolling a 2: [tex]\( \frac{1}{6} \)[/tex].
2. Theoretical Probability:
- A 6-sided die has 6 possible outcomes, and each outcome (rolling a 1, 2, 3, 4, 5, or 6) is equally likely.
- The probability of rolling any specific number, such as a 2, is [tex]\( \frac{1}{6} \)[/tex].
3. Experimental Probability:
- The given experimental probability of rolling a 2 is [tex]\( \frac{1}{15} \)[/tex], which deviates from the theoretical probability.
4. Concept of Matching Probabilities:
- The goal is to make the experimental probability [tex]\( \frac{1}{15} \)[/tex] closer to the theoretical probability [tex]\( \frac{1}{6} \)[/tex].
- Experimental probability becomes more accurate and closer to the theoretical probability as the number of trials increases, due to the Law of Large Numbers.
5. Evaluating the Options:
- Increasing the number of trials: By rolling the die more times, Jamie allows the experimental probabilities to even out and become closer to the theoretical probabilities. More trials help average out the variations and align the experimental results with expected outcomes.
- Decreasing the number of trials: Fewer trials can lead to higher variation and less reliable results, making it less likely that the experimental probability will match the theoretical probability.
- Increasing the number of sides on the die: Changing the die would alter the theoretical probability, as more sides would change the probability of rolling a specific number to [tex]\( \frac{1}{\text{number of sides}} \)[/tex].
- Decreasing the number of sides on the die: Similarly, changing the die to a different number of sides would also change the theoretical probability to [tex]\( \frac{1}{\text{number of sides}} \)[/tex].
6. Conclusion:
- The best action Jamie can take to make his experimental results more closely match the theoretical probability is to increase the number of trials. This will reduce the effect of random fluctuations and allow the experimental probability to converge more closely to the theoretical probability.
### Answer:
He can increase the number of trials.
