Question

josiah conducts an experiment that has 4 possible outcomes. sally conducts an experiment that has 10 possible outcomes. the students conduct 50 trials each. which statement best compares the two experiments? josiah and sally have the same likelihood of the experimental results being close to the predicted results because they used the same number of trials. josiah and sally have the same likelihood of the experimental results being close to the predicted results because the outcome of either experiment is unrelated to the outcome of the other experiment. sallys results are more likely to be close to the predicted results because she had a larger number of possible outcomes. josiahs results are more likely to be close to the predicted results because he had a smaller number of possible outcomes.

Explanation:

Step1: Understand the relationship between number of outcomes and likelihood

In probability, when the number of trials is fixed, a smaller number of possible outcomes means each outcome has a higher probability in a single trial. With more trials (here fixed at 50 for both), the experimental results for the experiment with fewer outcomes (Josiah's 4 - outcome experiment) are more likely to be close to the predicted (theoretical) results. For example, if we consider simple probability like coin - toss (2 outcomes), with more trials, the experimental probability gets closer to the theoretical 0.5.

Step2: Analyze each option

• Option 1: Just having the same number of trials doesn't mean the same likelihood. The number of outcomes also matters.
• Option 2: The outcome of one experiment is related to its own number of outcomes when comparing the likelihood of experimental results being close to predicted.
• Option 3: A larger number of possible outcomes (Sally's 10) means each outcome has a lower probability in a single trial. So, it's less likely for her experimental results to be close to predicted compared to Josiah.
• Option 4: Since Josiah has a smaller number of possible outcomes (4 < 10), with the same number of trials (50), his results are more likely to be close to the predicted results.

Answer:

Josiah's results are more likely to be close to the predicted results because he had a smaller number of possible outcomes.