What this calculator covers
The calculator handles two common probability situations: independent-event combinations and binomial probabilities. These are useful for quick checks, but only when the independence and constant-probability assumptions are reasonable.
Example
If event A has a 40% probability and independent event B has a 25% probability, the chance that both happen is 0.40 x 0.25 = 0.10, or 10%. The chance that at least one happens is 1 - (0.60 x 0.75) = 55%.
Common formulas
- A and B: P(A and B) = P(A) x P(B) for independent events.
- A or B: P(A or B) = P(A) + P(B) - P(A and B) for independent events.
- At least one: 1 - (1 - p)^n.
- Binomial: C(n,k) p^k (1-p)^(n-k), summed across a range when needed.
Limitations
Do not use this calculator for dependent draws without replacement, changing probabilities, Bayesian updating, survival analysis or risk models where the events are not independent.
References
- NIST/SEMATECH e-Handbook of Statistical Methods - statistical methods reference, accessed 2026-05-17.
FAQ
What is an independent event?
Events are independent when the outcome of one event does not change the probability of the other event.
What is a binomial probability?
A binomial probability models the number of successes in a fixed number of independent trials with the same success probability.
Can this model dependent events?
No. If probabilities change after each draw or event, use a method that matches that sampling process.
Last reviewed: 2026-05-17