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Probability: Theoretical and Experimental

5 min readGrade 6 · Data & Probability

A fair coin should land heads half the time. But if you flip it 10 times, you might get 7 heads. That's the difference between theoretical probability (what should happen) and experimental probability (what actually happens).

Theoretical probability

Assume all outcomes are equally likely. Count: favorable outcomes (what we want) and total possible outcomes. Probability = favorable ÷ total. For a fair die, rolling a 3: 1 favorable outcome out of 6 total, so P(3) = 1/6 ≈ 0.167 or about 16.7%.

Experimental probability

Perform an experiment many times and record results. Probability = times the event happened ÷ total trials. If you roll a die 60 times and get a 3 exactly 12 times, the experimental probability is 12/60 = 1/5 = 0.2 or 20%. (Close to the theoretical 1/6, but not exact.)

Law of Large Numbers

The more times you repeat an experiment, the closer the experimental probability gets to the theoretical probability. With just a few trials, they may differ a lot. With thousands of trials, they converge.

KEY VOCABULARY

Outcome — A possible result of an experiment (e.g., heads or tails for a coin flip).

Probability — The likelihood of an event occurring, expressed as a number from 0 (impossible) to 1 (certain).

Theoretical probability — The probability of an event based on reasoning (assuming equal likelihood).

Experimental probability — The probability of an event based on the results of an actual experiment.