Which approach to probability uses historical observations to estimate likelihood?

• A. Deriving probability from historical observations
• B. Assuming probability based on intuition
• C. Using a theoretical model with axioms
• D. Counting outcomes in a fair die only

Answer: (A)

The main concept is estimating likelihood from what has been observed in the past—the empirical, or frequency, approach. When you look at historical observations and count how often an event occurred relative to the total number of observations, that proportion serves as your estimate of probability. For example, if in past 100 trials the event happened 68 times, you’d estimate its probability as 0.68. As more data are collected, this empirical estimate tends to become more reliable due to the Law of Large Numbers.

This is why deriving probability from historical observations is the best fit here. It relies on actual data rather than assumptions. By contrast, relying on intuition uses subjective judgement, a theoretical model with axioms builds probability from abstract principles, and counting outcomes for a fair die assumes equal likelihood without invoking past data.