Question

during samuels experiment, the experimental probability was 0.25. what else must be true about the experiment?
the experimental probability of the outcome is \frac{1}{4}.
four trials were run during the experiment.
the experiment has four possible outcomes.
the theoretical probability of the outcome is \frac{1}{4}.

Explanation:

Step1: Recall the formula for experimental probability

Experimental probability \(P = \frac{\text{Number of times an event occurs}}{\text{Total number of trials}}\). Given \(P = 0.25=\frac{1}{4}\), and total number of trials \(n = 4\).

Step2: Analyze each statement

• For the statement “The experimental probability of the outcome is \(\frac{1}{4}\)”: Since experimental probability \(P=\frac{\text{Frequency of outcome}}{\text{Number of trials}}\), if \(P = 0.25=\frac{1}{4}\) and number of trials \(n = 4\), then the frequency of the outcome is \(1\).
• For the statement “Four trials were run during the experiment”: We know from the formula \(P=\frac{\text{Frequency of outcome}}{\text{Number of trials}}\), if \(P=\frac{1}{4}\), and assume frequency of outcome \(f = 1\), then number of trials \(n=\frac{f}{P}=\frac{1}{\frac{1}{4}}=4\).
• For the statement “The theoretical probability of the outcome is \(\frac{1}{4}\)”: There is no information about the nature of the experiment (e.g., fair - coin, fair - die etc.) to confirm theoretical probability. Theoretical probability is based on the nature of the sample space (e.g., for a fair - die \(P(\text{rolling a }1)=\frac{1}{6}\)). Here, we only know about experimental probability.
• For the statement “The experiment has four possible outcomes”: Experimental probability \(P = 0.25=\frac{1}{4}\) is calculated as \(\frac{\text{Frequency of a particular outcome}}{\text{Number of trials}}\). The number of possible outcomes is not related to the formula \(P=\frac{\text{Frequency of an outcome}}{\text{Number of trials}}\) used for experimental probability.

Answer:

The experimental probability of the outcome is \(\frac{1}{4}\) and four trials were run during the experiment.