Question

practicing with probabilities
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 \(P(E)=\frac{\text{Number of times event occurs}}{\text{Total number of trials}}\). Here, experimental probability \(P = 0.25=\frac{1}{4}\).

Step2: Analyze the theoretical probability formula

Theoretical probability \(P(T)=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}\). If the theoretical probability of an outcome is \(\frac{1}{4}\), and we know from the experimental probability context, when the experiment has four possible outcomes (since \(\frac{1}{4}\) is the probability value and in probability \(P=\frac{n(\text{favorable})}{n(\text{total})}\)), assuming all outcomes are equally - likely.

Answer:

The experiment has four possible outcomes.