Click Clear and then Run 10 trials 10 more times so that there are 100 trials. 1. How many of the outcomes are favorable? 2. What is the probability of landing on a 1 now? \( 1 / 100 \) I for the fraction bar. Please do not reduce on this problem.) 3. Compare the experimental probability with the theoretical probability of \( P(x=1)=\frac{1}{3} \). Do you think an experiment with 100 trials produces a probability is more reliable than an experiment with 10 trials? Yes \( \leftarrow \) (Click to view explanation) Check

Sure, let's address each of your questions step by step: --- ### **1. How many of the outcomes are favorable?** **Answer:** **1** **Explanation:** In your experiment, out of 100 trials, you observed the outcome you're interested in (landing on a 1) **1** time. Therefore, the number of favorable outcomes is **1**. --- ### **2. What is the probability of landing on a 1 now?** \(\frac{1}{100}\) *(Displayed as a fraction bar without reducing)* **Answer:** \[ \frac{1}{100} \] **Explanation:** Probability is calculated as the number of favorable outcomes divided by the total number of trials. Here, that's: \[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Trials}} = \frac{1}{100} \] You correctly represented the probability as \(\frac{1}{100}\). --- ### **3. Compare the experimental probability with the theoretical probability of \( P(x=1)=\frac{1}{3} \). Do you think an experiment with 100 trials produces a probability that is more reliable than an experiment with 10 trials?** **Your Answer:** **Yes** **Explanation:** - **Theoretical Probability:** The probability of landing on a 1 is \(\frac{1}{3}\) (~0.333). - **Experimental Probability:** In your experiment, the probability observed was \(\frac{1}{100}\) (0.01). While there's a significant difference between the experimental and theoretical probabilities in your results, the general principle holds that **a larger number of trials (100 in this case) tends to provide a more reliable and stable estimate of the true probability** compared to fewer trials (10). This is because larger samples reduce the impact of random variations and anomalies. However, it's also important to consider other factors that might affect the reliability of your experiment, such as: - **Randomness:** Ensure that each trial is independent. - **Bias:** Make sure there's no bias in how the trials are conducted. - **Consistency:** Ensure that the conditions remain consistent across all trials. In your specific case, observing only 1 favorable outcome out of 100 trials when the theoretical probability is \(\frac{1}{3}\) suggests that either more trials might be needed to approach the theoretical value, or there might be factors affecting the experiment's outcomes. --- **Summary:** Your answers to the questions are correct. Conducting more trials generally increases the reliability of experimental probability, bringing it closer to the theoretical probability. However, always ensure that the experimental setup is sound to obtain accurate and reliable results.