How to use this calculator
Use this tool only when A and B are independent: learning whether one occurred must not change the probability of the other. “Or” is inclusive, so either or both counts. “Exactly one” excludes the case where both occur. If the events are mutually exclusive, they are generally not independent; for dependent events you need their joint probability or conditional probabilities instead.
The formula
P(A and B) = P(A)P(B); P(A or B) = P(A) + P(B) − P(A)P(B)
Here p is a probability from 0 to 1, n is a whole number of attempts, C(a,b) counts combinations, and ∏ means multiply all the factors. The input labels define the other symbols.
A worked example
For independent events at 30% and 40%, both occur with probability 12%, and at least one occurs with probability 58%.
Does this predict what I will get?
No. It describes a probability under the rules you enter. A single run can differ from the average. A displayed rounded 100% may still be slightly below certainty unless the model includes a guarantee.
Where do the rates come from?
You enter them. Check the rules and rate disclosure for your exact outcome. We do not supply odds for real products, collect account details or fetch rates from a game or seller.