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Math — Probability

Probability Calculator

Enter two event probabilities to get both, either, neither and exactly one occurring.

Filed by The Statistics Desk  |  Method: independent-event probability
P(A and B)
—
Both events happen (independent).
Readout
P(A or B)—
P(neither)—
P(exactly one)—
P(not A)—
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Enter your figures above to see the step-by-step working.
Assumes independent eventsEverything computed client-side — nothing leaves this page

How the Probability Calculator Works

This calculator takes the probabilities of two independent events, A and B, and works out the common combinations: both happening, at least one happening, neither happening, and exactly one happening. Independent means one event does not affect the other — like two separate coin flips or dice rolls.

For independent events, the chance of both is the product of their probabilities; the chance of at least one is their sum minus that overlap; and the chance of neither is the product of their complements. Enter each probability as a percentage from 0 to 100.

P(A and B) = P(A) × P(B)   P(A or B) = P(A) + P(B) − P(A and B)

Frequently Asked Questions

What does "independent events" mean?

Two events are independent when the outcome of one has no effect on the other — for example flipping a coin and rolling a die. This calculator assumes independence; for dependent events the formulas differ.

Why is P(A or B) not just P(A) + P(B)?

Because simply adding them would double-count the cases where both happen. You subtract P(A and B) once to correct for that overlap.

How do I enter a probability?

Enter it as a percentage between 0 and 100. A one-in-four chance is 25, a coin flip is 50, and a certainty is 100.

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