Experimental Probability

Pre-Algebra · Axiom Academy

LESSON Experimental Probability Instead of just predicting a probability, run the trials, count what happens, and watch the results close in on the prediction. Experimental probability comes from doing the experiment, not just thinking about it. Each repetition is a trial ; you tally how often the event you care about shows up, then divide by the number of trials. Watch ten coin flips land one at a time — the running fraction of heads is the experimental probability so far. The experimental probability is a ratio you measure There are two probabilities in play, and they answer different questions. Theoretical probability is what should happen by counting equally-likely outcomes. Experimental probability is what did happen in your trials. For a fair coin they aim at the same target — yet on a short run they rarely match exactly. Counted from the model: 1 favorable side out of 2 equally-likely sides, so . It never changes. Measured from the run: 6 heads out of 10 flips, so . It depends on the trials. Here observed beats predicted by 10 percentage points — a perfectly ordinary wobble for only 10 flips. Both describe the same coin, so the experimental value hovers around — not far from — the theoretical one.

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