Probability Calculator
Use fractions or percentages to calculate independent events and repeated-trial probabilities.
Try an example
Events and trials must be independent.
Formulas & edge cases tested · 2026-10-20 · Calculation basis
Formulas, assumptions and checks
For independent events, P(A∩B)=P(A)×P(B). For n independent trials with the same success probability p, P(at least one success)=1−(1−p)ⁿ. Sampling without replacement is not covered.
Checked: 0% and 100%, fractions, coin-flip combinations, repeated trials, empty and invalid inputs, and tiny probabilities.
OpenStax · Independent events ↗How to use Probability Calculator
Enter values such as 50% or 1/6 for two independent events. Repeated-trial mode calculates at least one success, all successes or no successes for independent trials with the same probability. Dependent events and sampling without replacement are not covered.
Displayed values follow the definitions stated above.
Check that the events are independent first
This calculator assumes that whether event A occurs does not change the probability of event B. It is suitable for independent trials such as separate coin flips, not problems that require conditional probability.
At least one event: P(A∪B)=P(A)+P(B)−P(A)×P(B).
Recommended steps
- Enter each probability between 0% and 100%.
- Check whether the result of one event changes the other probability.
- Choose the both-events or at-least-one result for your question.
How to interpret the result
- For independent events, the probability of both cannot exceed either individual probability.
- The at-least-one formula subtracts the overlap counted twice by simple addition.
- Sampling without replacement usually changes later probabilities and needs conditional probability.
Frequently asked questions
What are independent events?
They are events where knowing the outcome of one does not change the probability of the other.
Why can I not simply add the two probabilities?
The case where both occur is counted twice, so the overlap must be subtracted once.
Can this calculate lottery odds?
It can combine independent trial probabilities, but draws without replacement need a formula based on combinations and the sampling rules.