Question

james conducted an experiment with 4 possible outcomes. he determined that the experimental probability of event a happening is 10 out of 50. the theoretical probability of event a happening is 1 out of 4. which action is most likely to cause the experimental probability and theoretical probabilities for each event in the experiment to become closer?
performing the experiment again, stopping immediately after each event occurs once
including a fifth possible outcome
completing the experiment many more times and combining the results to the trials already done
removing the last 10 trials from the experimental data

Explanation:

Step1: Understand experimental probability concept

Experimental probability is based on the results of actual trials. As the number of trials increases, the experimental probability tends to get closer to the theoretical probability.

Step2: Analyze each option

• Removing the last 10 trials from the experimental data: This would reduce the number of trials, making the experimental probability less reliable (further from theoretical probability).
• Performing the experiment again, stopping immediately after each event occurs once: This gives a very small number of trials (only 4 trials if there are 4 outcomes, assuming one trial per outcome), so the experimental probability won't be accurate.
• Including a fifth possible outcome: This changes the nature of the experiment (the theoretical probability is based on 4 outcomes), so it won't make the experimental probability of event A (based on 4 - outcome experiment) closer to the theoretical value.
• Completing the experiment many more times and combining the results to the trials already done: Increasing the number of trials (by doing many more trials and combining) will make the experimental probability (calculated as \(P=\frac{\text{Number of times event A occurs}}{\text{Total number of trials}}\)) approach the theoretical probability.

Answer:

Completing the experiment many more times and combining the results to the trials already done