When the two disagree
A die is rolled 15 times. A 4 shows 5 times. Is the die fair? A fair die is equally likely to show each face.
We cannot tell yet. A fair die can show five 4s in 15 rolls.
Two figures, two questions
Real rolls give 5/15 = 1/3, about 0.33. The die's six equal faces give 1/6, about 0.17. The two are not the same number.
The observed chance reports what happened. The worked-out chance reports what the set-up allows. With more rolls, the two chances usually get closer.
Experimental — the observed chance, from real rolls. Theoretical — the worked-out chance, from the die's faces.
| Figure | Comes from | Value |
|---|---|---|
| Experimental | 15 rolls | 0.33 |
| Theoretical | the die's 6 faces | 0.17 |
Roll the die 10000 times. The gap is usually much smaller. It still does not have to be zero.
Rule: Real rolls give one figure. The die's faces give another. With few rolls a gap is normal. It does not prove the die is unfair.
Drag the rolls. Watch the gap.
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