🎲 Probability Calculator
Compute probabilities of independent events: P(A∩B), P(A∪B), and at-least-once probability 1-(1-p)^n — all in your browser.
Two independent events
At-least-once probability
Enter probabilities and trials to see results.
About the Probability Calculator
This calculator computes three common probability values for independent events: the joint probability that both A and B happen, the union probability that at least one of A or B happens, and the at-least-once probability that an event with single-trial probability p occurs at least once across n independent trials.
Formulas
- Joint (A and B):
P(A∩B) = P(A) × P(B)(independence assumed) - Union (A or B):
P(A∪B) = P(A) + P(B) − P(A∩B) - At least once:
P(at least one) = 1 − (1 − p)^n
How to use
- Enter P(A) and P(B) as values between 0 and 1 (e.g. 0.5 for 50%).
- Enter p (single trial probability) and n (number of trials) for the at-least-once calculation.
- Click Calculate. All three results appear below.
Frequently asked questions
Why is P(A∩B) just the product? Because the calculator assumes A and B are independent. If they are dependent, you must use the conditional probability formula P(A∩B) = P(A) × P(B|A) instead.
What does "at least once" mean? It is the probability that an event happens one or more times across n independent trials. It is the complement of "never happens", computed as 1 − (1 − p)^n.
Can probabilities be greater than 1? No. Inputs outside the range [0, 1] are rejected as invalid.
Why does the union subtract the intersection? Otherwise events A and B would both contribute the joint occurrence, double-counting it.