Definition: Theoretical probability is what should happen based on equally likely outcomes, while experimental probability is what actually happened in repeated trials.
What is the difference?
Theoretical probability uses reasoning about the sample space. Experimental probability uses data from real trials: the number of times the event occurred divided by the number of trials.
How do they compare?
A fair 6-sided die lands on 5 with theoretical probability 1/6, about 0.167. Mathbot rolls it 50 times and gets a 5 on 11 rolls. The experimental probability is 11 / 50 = 0.22.
Why do they differ?
Small samples vary. After 600 rolls, the experimental value will typically be much closer to 0.167. This is the law of large numbers.
How do you predict?
Use the probability times the number of trials. Expect about 0.167 x 300, roughly 50 fives in 300 rolls.
What is a common mistake?
Expecting exact agreement. If the theoretical chance is 1/6, rolling 60 times does not guarantee exactly 10 fives. Another error is to treat the experimental result as the true probability after only a few trials.