Independent Probability Calculator
Combine two independent event probabilities for both, either, neither or exactly one.
Your result
MATHEnter your values and select calculate.
On this page How it works & practical examples
How to use the Independent Probability Calculator
Use probabilities between 0% and 100% and confirm that the independence assumption is appropriate. Independence means that learning whether one event occurred does not change the other event’s probability. The tool calculates the intersection by multiplication and uses complementary outcomes to report other combinations. The four possibilities should be understood as outcomes of the same two-event model.
The calculation
Worked example
For independent events with probabilities 50% and 25%, both occur with probability 12.5%, at least one with 62.5%, neither with 37.5%, and exactly one with 50%.
Assumptions and limits
Dependent events need additional information such as conditional probabilities; these formulas should not be applied automatically. “At least one” includes the case in which both events occur, whereas “exactly one” excludes it. Values supplied as estimates produce estimated outputs, even though the arithmetic itself is straightforward.
Common questions
Are mutually exclusive events independent?
Generally no, unless one has zero probability. If one excludes the other, the joint probability is zero rather than the product of two positive probabilities.
What is the difference between either and exactly one?
Here “at least one” includes both. “Exactly one” counts A without B or B without A.