Probability Calculator
Calculate the probability of a single event, or combine two independent events with AND/OR logic.
AND vs. OR for combining probabilities
This calculator assumes both events are independent — meaning the outcome of one doesn't affect the other, like two separate dice rolls. For 'AND' (both events happening), independent probabilities multiply together. For 'OR' (at least one happening), you add the individual probabilities and subtract their overlap, since simply adding would double-count the case where both happen.
A classic example: rolling a 6 on one die (1/6) AND rolling a 6 on a second die (1/6) gives 1/6 × 1/6 = 1/36 — much less likely than either event alone, which makes sense since both specific outcomes need to occur together.
What 'independent events' means
Independent events don't influence each other's outcome — a coin flip doesn't affect the next coin flip, and rolling one die doesn't affect another. This is different from dependent events, like drawing cards from a deck without replacement, where each draw changes the probabilities for the next one.
This calculator's formulas are only valid for independent events — dependent event calculations require a different, more involved approach that accounts for how earlier outcomes change later probabilities.
Frequently asked questions
What does it mean for two events to be independent?
Independent events don't affect each other's outcome — like separate coin flips or dice rolls. This is different from dependent events, such as drawing cards without replacement, where earlier outcomes change later probabilities.
Why do I subtract the overlap when calculating OR probability?
Simply adding the two probabilities would double-count the outcome where both events happen — subtracting the overlap (the AND probability) corrects for that double-counting.