Which probability is derived from observed data rather than theory?

• A. Theoretical Probability
• B. Empirical Probability
• C. Conditional Probability
• D. Joint Probability

Answer: (B)

Observing data to estimate how often something happens is empirical probability. It uses relative frequency: count how many times the event occurs and divide by the total number of observations. This makes the probability a reflection of what actually happened in the data, not just what a model predicts.

For example, if you record each roll of a die and find a 4 appears 18 times out of 120 rolls, the empirical probability of rolling a 4 is 18/120 = 0.15. This differs from the theoretical probability of 1/6 (about 0.1667) because the data come from a finite sample.

Theoretical probability, by contrast, comes from assumptions about the process (like all outcomes being equally likely). Conditional and joint probabilities describe probabilities under relationships or combinations of events, and while you can estimate them from data, they aren’t defined as “based on observed data” in the same sense as empirical probability.