How it works
This calculator combines the probabilities of two events. For independent events, where one happening does not change the chance of the other (two coin flips, two dice), the chance of both is the product of the two probabilities.
For mutually exclusive events, which cannot happen together (rolling a 1 and a 6 on the same die), the chance of both is zero and the chance of either is simply the sum.
The complement rule gives the chance an event does not happen: P(not A) = 1 − P(A). “Neither” is the complement of “A or B”.
Formula
P(A and B) = P(A) × P(B) if independent · P(A or B) = P(A) + P(B) − P(A and B) · P(not A) = 1 − P(A)
Questions people ask
What is the difference between independent and mutually exclusive?
Independent events can both happen and do not affect each other. Mutually exclusive events can never happen at the same time. Two events with nonzero probability cannot be both independent and mutually exclusive.
Why subtract P(A and B) when finding P(A or B)?
Adding P(A) and P(B) counts the overlap, where both happen, twice. Subtracting it once corrects the double count.
What if my events are dependent?
Then P(A and B) = P(A) × P(B given A), and you need the conditional probability. This calculator covers the independent and mutually exclusive cases.