Question

nadine conducted an experiment with four possible outcomes. trevor conducted the same experiment, but he doubled the number of trials. which statements are true? select two options. ☐ trevor has more experimental outcomes than nadine. ☐ trevor’s sample space is greater than nadine’s. ☐ trevor’s experimental probability is more likely closer to the theoretical probability than nadine’s. ☐ nadine’s experimental probability is more likely closer to the theoretical probability than trevor’s. ☐ nadine has more experimental outcomes than trevor.

Explanation:

• Experimental outcomes depend on trials, but sample space (possible outcomes) is fixed by the experiment (4 outcomes), so Trevor doesn't have more experimental outcomes or larger sample space.
• Larger number of trials (Trevor doubled trials) makes experimental probability closer to theoretical probability (law of large numbers). So Trevor’s experimental probability is more likely closer to theoretical than Nadine’s. The other wrong options misinterpret sample space or experimental outcomes.

Answer:

• Trevor’s experimental probability is more likely closer to the theoretical probability than Nadine’s. (This is one correct option. The other correct option is that neither has more experimental outcomes or larger sample space, but among the options, the other correct one related to probability: Wait, the options given: Wait, the two correct options are: Wait, re - evaluating:

1. "Trevor’s experimental probability is more likely closer to the theoretical probability than Nadine’s." (Because more trials → closer to theoretical, by law of large numbers)
2. The other: Wait, the options about experimental outcomes and sample space are wrong. Wait, the problem says "select two options". Wait, maybe I made a mistake. Wait, sample space is the set of possible outcomes, which is 4 for both (same experiment), so sample space is same. Experimental outcomes: number of times each outcome occurs in trials. Trevor has more trials, so he has more experimental outcomes? Wait, no: experimental outcomes are the results of each trial. If Nadine did n trials, Trevor did 2n trials. So Trevor has more experimental outcomes (since 2n > n). Oh! I made a mistake earlier. So:

• "Trevor has more experimental outcomes than Nadine." (Because he has more trials, so more individual outcomes from trials)
• "Trevor’s experimental probability is more likely closer to the theoretical probability than Nadine’s." (Because more trials → closer to theoretical)

So the two correct options are:

1. Trevor has more experimental outcomes than Nadine.
2. Trevor’s experimental probability is more likely closer to the theoretical probability than Nadine’s.