Empirical probability is defined as the probability of an event based on which source?

• A. Observed frequencies in repeated trials
• B. The probability of an event based on theoretical calculations
• C. The parameter of a population
• D. A subjective belief about likelihood

Answer: (A)

Empirical probability uses observed frequencies from repeated trials to estimate how likely an event is. You tally how often the event occurs and divide by the total number of trials, giving the relative frequency as the probability.

For example, if you flip a coin 100 times and observe 53 heads, the empirical probability of heads is 53/100 = 0.53. With more trials, this estimate tends to the theoretical probability, illustrating the idea behind the law of large numbers.

The other sources describe different concepts: theoretical probability relies on mathematical calculations under assumed rules; a population parameter is the true long-run proportion in the whole population; a subjective belief is a personal guess or guesswork about likelihood.