Experimental vs Theoretical
Compare observed relative frequencies with a probability model. With independent trials and fixed outcome probabilities matching the model, larger samples usually give closer estimates. A particular longer run can still be farther away.
What a learner can do afterwards
- Roll a fair six-sided die 60 times and compare observed counts with the expected 10 per number
- Explain why observed shares can differ from theoretical probabilities, can match them exactly, and tend to be closer in larger independent samples under the same model
- Predict what would happen if the experiment were repeated 600 times instead of 60
1 · Read
You want a die to treat everyone the same. A fair six-sided die has six equally likely faces, so the theoretical probability of a 3 is 1 in 6. Experimental probability is what you count: the number of 3s divided by the number of rolls. Probability times trials gives the expected count, so 60 rolls of a fair die are expected to give about 10 of each number. To judge a run, compare each observed count with the expected 10.
Zara flips a fair coin 10 times and gets 7 heads. That is not 50:50, but a fair coin can easily do that. With only 10 flips, results bounce around a lot. About half of a long run of fair flips is expected to be heads, so over 600 flips the share would very likely land much closer to half.
With independent trials and a fixed chance, larger samples usually give shares closer to that chance. Independent means one result does not change the chance of another. A longer run can still be farther off.
With independent trials and a fixed chance, larger samples usually give closer shares. A particular longer run can still be farther away.
Rewritten readings were written for this dataset.
2 · Watch
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Where it sits
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Where this leads
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18 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.