Probability Calculator
Enter the probabilities of two independent events to find their combined and complementary probabilities.
Assumes A and B are independent: P(A) × P(B).
- 1
P(not A) = 1 − P(A)
1 − 0.5 = 0.5 - 2
P(not B) = 1 − P(B)
1 − 0.3 = 0.7 - 3
P(A and B) = P(A) × P(B)
0.5 × 0.3 = 0.1500A and B are assumed independent, so their joint probability is the product.
Formula
How this is calculated
You enter two probabilities, P(A) and P(B), each a number between 0 (the event never happens) and 1 (it always happens). These are unitless fractions; multiply by 100 to read them as percentages. The calculator treats A and B as independent, meaning the outcome of one has no effect on the other — think of two separate coin flips or two distinct dice.
The joint probability that both occur is the product P(A) × P(B), because independence lets the two chances multiply directly. The probability that at least one occurs uses the inclusion–exclusion rule: P(A) + P(B) − P(A and B); subtracting the overlap prevents double-counting the cases where both happen. Each complement, such as P(not A) = 1 − P(A), is simply the remaining share of certainty.
The key assumption is independence. If the events are dependent (one influences the other) or mutually exclusive (they cannot both occur, so P(A and B) = 0), these results no longer apply and you would need conditional probabilities instead.
About this calculator
Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain). This calculator works with two independent events, A and B, meaning the outcome of one does not affect the other — like rolling two separate dice or flipping two coins.
For independent events, the probability that both happen is the product P(A) × P(B). The probability that at least one happens uses the addition rule with the overlap removed: P(A) + P(B) − P(A and B). The complement, P(not A) = 1 − P(A), gives the chance that an event does not occur. If your events are dependent or mutually exclusive, these formulas change accordingly.
Frequently asked questions
Two events are independent when the occurrence of one does not change the probability of the other. For independent events, P(A and B) equals P(A) × P(B).
Adding P(A) and P(B) double-counts the outcomes where both occur. Subtracting P(A and B) removes that overlap so each outcome is counted once.
If A and B cannot both happen, then P(A and B) = 0, so P(A or B) simply becomes P(A) + P(B). This calculator assumes independence rather than mutual exclusivity.
Also known as
TG we-Calculate Editorial Team. (2026). Probability Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/probability-calculator
TG we-Calculate Editorial Team. "Probability Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/probability-calculator.
TG we-Calculate Editorial Team, "Probability Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/probability-calculator
@misc{wecalculate_probability_calculator, title = {Probability Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/probability-calculator}}, year = {2026}, note = {TG we-Calculate} }
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