Probability Calculator
Calculate the chance that two independent events both or either occur.
How to use Probability Calculator
Calculates intersection and union probabilities for two independent events. Do not use these formulas when the events affect each other.
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.