Probability calculator for outcomes, repeated trials and independent events
Use counts for an equally likely sample space or enter two known independent probabilities. HitEquals returns the event, complement, repeated-trial or intersection and union probabilities with percentages and odds.
Inputs used by this calculator
Probability Calculator uses the fields below. The starting values reproduce the page example; replace them with values from the same units and time period before using the result.
| Input | Starting example | Accepted value | How it is used |
|---|---|---|---|
| Probability model | Equally likely outcomes and repeated trials | Equally likely outcomes and repeated trials · Two independent events | Chooses which Probability Calculator method or unknown the engine evaluates. |
| Favorable outcomes | 1 | 0 to 1000000000 | Supplies the favorable outcomes quantity used by the published equation or result breakdown. |
| Total equally likely outcomes | 6 | 1 to 1000000000 | Selects the unit or conversion path used by Probability Calculator. |
| Independent trials | 3 | 1 to 1000000 | Supplies the independent trials quantity used by the published equation or result breakdown. |
| Probability of A (%) | 40 | 0 to 100 | Supplies the probability of a (%) quantity used by the published equation or result breakdown. |
| Probability of B (%) | 30 | 0 to 100 | Supplies the probability of b (%) quantity used by the published equation or result breakdown. |
Probability from equally likely outcomes
Count the outcomes that satisfy the event and divide by all possible equally likely outcomes. The favorable count cannot exceed the total.
P(E)=n(E)÷n(S)Complement probability
The complement contains every outcome outside the event. Event and complement probabilities always sum to one.
P(E′)=1−P(E)Repeated independent trials
For at least one success, first calculate the chance of no successes and subtract it from one.
P(at least one)=1−(1−p)^nTwo independent events
Independence means learning whether A occurred does not change the probability of B. Multiply for both events and subtract the overlap when finding either event.
P(A∩B)=P(A)P(B)P(A∪B)=P(A)+P(B)−P(A∩B)Worked die example
One specified face among six equally likely faces gives p=1/6. Three independent rolls have no-six probability (5/6)³, so at least one six is about 42.13%.
Assumptions and misuse
Replacement often supports independence; drawing without replacement usually does not. A mathematical result is only as reliable as its sample-space and independence assumptions.
Probability scale
| Probability | Interpretation | Complement |
|---|---|---|
| 0 | Impossible in the model | 1 |
| 0.25 | One in four | 0.75 |
| 0.5 | Even chance | 0.5 |
| 1 | Certain in the model | 0 |
Frequently asked questions
What is a favorable outcome?
An outcome included in the event being measured.
Can probability exceed 100%?
No. A valid probability is between 0 and 1, or 0% and 100%.
What does at least one mean?
One or more successes across the entered trials.
Why use the complement rule?
It often replaces many separate success cases with one no-success calculation.
Are mutually exclusive events independent?
Usually no. If one nonzero event occurs, the other cannot occur.
Does this predict real outcomes?
No. It evaluates the assumptions and probabilities entered.
What to keep in mind
The outcome model assumes outcomes are equally likely and trials are independent. Real-world dependence, biased sampling, changing conditions and uncertain input probabilities require a different model.
Results are rounded for display in US format, with money in dollars and cents; CSV exports keep full calculation precision. This is a calculation summary, not an official certificate.