Mathematics — first biennium · Lesson
Classical probability comes from a model of equally likely outcomes; empirical probability is the observed relative frequency. In finitely many trials they need not match exactly.
Prerequisites: Relative frequencies and classical probability
Goal: Compare observed relative frequency and theoretical probability without confusing a finite sample with the model.
In this lesson: Compare observed relative frequency and theoretical probability without confusing a finite sample with the model.
New concept: Theoretical probability comes from a model; empirical relative frequency comes from observed data: successes/trials. With many trials the empirical value often approaches the theoretical one, but in a finite sample they need not be equal.
How to proceed: Keep the two sources separate: experimental counts give empirical frequency, while the theoretical model gives classical probability.
You can already assume: Relative frequencies and classical probability.
f_rel = observed frequency · P(E) = theoretical probability
The two bars compare observed relative frequency and theoretical probability on the same 0-to-1 scale.
Completed exercises: 0/5 · Correct on first attempt: 0
Keep the two sources separate: experimental counts give empirical frequency, while the theoretical model gives classical probability.
Data / situation: A fair die is rolled 30 times and a 6 appears 4 times.
ConceptStep separates what is required from what is recommended or useful as reinforcement. Only required prerequisites block your progress.
Relationships: solid line = required · dashed line = recommended · dotted line = reinforcement.