StatReasonWhat this answers
This calculator applies the three basic rules for combining event probabilities: the addition rule for "A or B", the multiplication rule for "A and B" when the events are independent, and the complement rule for "not A". Picking the wrong identity for your situation is one of the most common probability mistakes, so this tool keeps the three clearly separated rather than offering one all-purpose formula.
How it is calculated
The union rule is P(A) plus P(B) minus P(A and B), subtracting the overlap once so it is not double-counted; if you do not supply P(A and B) directly, this calculator assumes independence and computes it as P(A) times P(B). The complement rule is simply 1 minus P(A), since an event and its complement together must account for all of the probability.
Worked example
For a fair six-sided die, let A be "rolling an even number" (P(A)=.5) and B be "rolling a number greater than 3" (P(B)=.5), with P(A and B)=.25 (rolling 4 or 6). The union rule gives P(A or B) = .5 + .5 − .25 = .75, matching a direct count of the four qualifying outcomes (2, 4, 5, 6) out of six.
Assumption audit
Common mistakes
A frequent mistake is applying the simple multiplication rule (P(A) times P(B)) to events that are not actually independent, silently producing a wrong intersection probability. Another is forgetting to subtract the overlap in the union rule, effectively double- counting outcomes that belong to both events. A third is entering an intersection larger than either individual event's probability, which is not just wrong but logically impossible, since the intersection can never exceed either one.
Limitations
This calculator handles the two-event case with basic identities only; more complex situations (three or more events, conditional dependencies) require the full formulas found in the Conditional Probability and Bayes Theorem calculators.