Probability Calculator
Combine the odds of two independent events — both, either, neither or only one.
How to use the Probability Calculator
- Enter the probability of each event (as 0–1, or as a percentage).
- The tool assumes the two events are independent.
- Read the chance of both, either, neither, and only one.
Both = A × B · Either = A + B − A×B
About the Probability Calculator
This calculator combines the odds of two events to show four outcomes: both happening, either one happening, neither happening, and only the first happening. It uses both = A x B and either = A + B - A x B, with neither and only-A derived from the same values. You can enter each probability as a decimal from 0 to 1 or as a percentage, and the tool reads either format.
The key assumption is independence: the two events must not affect each other. Flipping a coin and rolling a die are independent, so the simple multiply-and-add rules apply exactly. Drawing two cards without replacing the first is not independent, because the first draw changes the odds of the second. For those dependent cases the true probabilities differ from what this tool reports.
Enter your two probabilities to see all four combined results at once. If your events are genuinely linked, adjust the second probability to its conditional value first, or treat the output as an approximation. For single-event percentages, use the Percentage Calculator, and for spread in a dataset see the Standard Deviation Calculator.
Frequently asked questions
How does this calculate combined probability?
For both events it multiplies the two probabilities (A x B). For either event it uses A + B minus A x B, which avoids double-counting the overlap. Neither and only-A are worked out from the same two values.
Can I enter percentages or decimals?
Either works. You can type a probability as a decimal between 0 and 1, such as 0.5, or as a percentage such as 50. The tool interprets both, so use whichever form your figures come in.
What does the independence assumption mean?
It means each event happens without affecting the other, like two separate coin flips. The multiply-and-add formulas are exact only for independent events. If one outcome changes the odds of the other, the events are dependent and the results will differ.
What if my events are dependent?
Then this tool only approximates the answer. For dependent events you should use the conditional probability of the second event given the first. Enter that adjusted value, or treat the combined figures here as a rough guide rather than exact.
What does the neither outcome mean?
Neither is the chance that both events fail to happen. It is calculated as the probability that A does not occur multiplied by the probability that B does not occur, again assuming the two events are independent.