Calculate theoretical probability and expected frequency from equally likely outcomes with percent conversion, assumptions and checks.
Choose an example or type the known values, then calculate to see the answer and working.
Assume the eight outcomes are distinct and equally likely, with 40 independent trials planned.
Estimate the sign, scale, range or likely form of the answer before calculating. A prediction makes an input error easier to notice.
Probability = 3 ÷ 8 = 0.375.
Convert to a percentage: 0.375 × 100% = 37.5%.
Expected frequency in 40 trials = 0.375 × 40 = 15.
Check that 0.375 lies between zero and one and that 15 is a plausible part of 40.
Theoretical probability compares favourable outcomes with the complete set of equally likely outcomes. This calculator returns the probability as a decimal and percentage, then multiplies it by a chosen number of trials to estimate expected frequency. An expectation is a long-run model, not a promise about what must occur in one short experiment.
Use it when outcomes are mutually exclusive, the list is complete and each outcome is equally likely. Enter favourable outcomes as a whole-number count no greater than the total. The trials field creates an expected frequency for repeated independent trials. Do not use simple favourable-over-total reasoning for biased spinners, survey responses or events with unequal probabilities unless the model has been adjusted.
Zero represents impossibility under the model and one represents certainty. A result outside this range signals invalid counts or a calculation error.
An expectation of 7.5 describes the long-run average across repeated sets of trials. A single experiment still produces a whole observed count and may differ.
A fair die has equally likely faces; a real-world event may not. Correct division cannot repair an unsuitable outcome model, so name fairness and independence where they matter.
| Mistake | Why it fails | Better check |
|---|---|---|
| Counting overlapping outcomes twice | The favourable count can then exceed the real sample space or double-count one result. | Define mutually exclusive elementary outcomes before counting. |
| Assuming every list is equally likely | Weather categories or survey answers may have different underlying probabilities. | Use favourable over total only when equal likelihood is justified. |
| Treating expectation as certainty | Fifteen expected successes does not guarantee exactly fifteen in the next forty trials. | Compare observed frequency with expectation across many repetitions. |
Yes. The probability is one, or 100%, under the stated model.
The probability and expected frequency are zero, meaning the event is impossible within the listed sample space.
No. Products, unions and conditional probabilities require additional relationships. This page handles one favourable-over-total model.
The result points to related practice, but the best next step depends on what the learner could explain without help.