Experimental probability is the ratio of the number of times an event occurs to the total number of trials performed. It is based on actual data, not theory. Flip a coin 100 times. If it lands heads 53 times, the experimental probability of heads is 53/100, or 0.53. The theoretical probability is 0.5. They are close but not identical.

Experimental probability varies from trial to trial. Run the experiment again and you get a different result. Flip the coin another 100 times and you might get 48 heads. The experimental probability is 0.48. The more trials you run, the closer the experimental probability gets to the theoretical probability. That is the law of large numbers.

Experimental vs. theoretical probability

• Experimental: based on observed data.
• Theoretical: based on equally likely outcomes.
• Experimental varies; theoretical is fixed.
• Experimental approaches theoretical with more trials.
• Both are expressed as fractions, decimals, or percentages.

Experimental probability is used when theoretical probability is hard to calculate. What is the probability that a new drug cures a disease? You cannot calculate it from first principles. You run a clinical trial. The experimental probability is the proportion of patients who improve. What is the probability that a machine produces a defective part? You sample the production line. The experimental probability is the defect rate. Experimental probability is empirical. It is based on observation. It is the foundation of statistics. It tells you what actually happened, not what should happen in theory. The two are related, but they are not the same. Theory predicts. Experiment observes. Both are useful.