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 coin is tossed 30 times and 17 heads are observed.
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.