OR Probability Calculator — P(A or B)
Find the probability that event A, event B, or both occur. Enter P(A) and P(B) and choose whether the events are independent (the classic roll-two-dice scenario) or mutually exclusive (they cannot both happen at once).
Relationship between A and B
Probability that event A, event B, or both occur
- 1
Joint probability P(A ∩ B) = P(A) × P(B)
0.6 × 0.4 = 0.24 - 2
Addition rule P(A or B) = P(A) + P(B) − P(A ∩ B)
0.6 + 0.4 − 0.24 = 0.7600
How does this calculator work?
P(A or B) = P(A) + P(B) − P(A and B). For independent events P(A and B) = P(A) × P(B); for mutually exclusive events P(A and B) = 0. Enter both probabilities and the event relationship to get the union probability, the joint probability, and the probability that neither occurs.
Formula
How this is calculated
The addition rule of probability states that P(A or B) = P(A) + P(B) − P(A and B). Subtracting the joint probability prevents double-counting outcomes where both events happen simultaneously. The formula changes based on the relationship between the events.
For independent events — where the outcome of one does not influence the other — the joint probability is simply the product P(A) × P(B). Classic examples are rolling two separate dice or drawing with replacement from a deck. For mutually exclusive events — where A and B cannot occur at the same time — the joint probability is exactly 0, so P(A or B) collapses to P(A) + P(B). Examples include rolling a 1 vs. rolling a 2 on a single die.
The probability space bar below shows how the total probability of 1 is divided: A-only outcomes, outcomes where both happen, B-only outcomes, and outcomes where neither occurs. If your events are neither fully independent nor mutually exclusive (for example, correlated measurements), you would need to supply P(A and B) directly — an extended version of this calculation.
Frequently asked questions
The addition rule states P(A or B) = P(A) + P(B) − P(A and B). Subtracting the joint probability removes the double-count of outcomes where both events happen at once.
Choose mutually exclusive when the two events cannot both occur in the same trial — for example, drawing a red card vs. drawing a black card from a standard deck, or a patient having disease A vs. disease B if they are diagnosed as distinct conditions. In that case P(A and B) = 0.
No — probabilities are always between 0 and 1. If P(A) + P(B) > 1 for mutually exclusive events, those probabilities are inconsistent (the events would together claim more than 100% of outcomes), and the calculator returns no result.
Also known as
TG we-Calculate Editorial Team. (2026). OR Probability Calculator — P(A or B) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/or-probability-calculator
TG we-Calculate Editorial Team. "OR Probability Calculator — P(A or B)." TG we-Calculate. 2026. https://we-calculate.com/calculator/or-probability-calculator.
TG we-Calculate Editorial Team, "OR Probability Calculator — P(A or B)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/or-probability-calculator
@misc{wecalculate_or_probability_calculator, title = {OR Probability Calculator — P(A or B)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/or-probability-calculator}}, year = {2026}, note = {TG we-Calculate} }
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