Which statement best describes theoretical probability?

• A. The likelihood of an outcome derived without data using mathematical reasoning
• B. The likelihood determined by repeated trials
• C. The probability of an outcome that cannot occur
• D. The probability that changes with sample size

Answer: (A)

The idea behind theoretical probability is to determine how likely an outcome is using a mathematical model, not by looking at data. It relies on the sample space—the set of all possible outcomes—and counts how many outcomes are favorable, then forms a ratio of favorable outcomes to total outcomes under explicit assumptions (like equal likelihood for each outcome). This gives a probability before any experiment is performed. For a fair six‑sided die, there are six equally likely outcomes and one that matches the event, so the theoretical probability is 1/6. This is different from probability based on data from trials, which is empirical and can change as you collect more observations. The probability of an event that cannot occur is zero, which isn’t about predicting a real, possible outcome. And a probability that changes with sample size describes how empirical estimates behave as more data is gathered, not the mathematically derived probability. So reasoning about likelihood without data using a clear model best matches theoretical probability.