Statistics · Probability

Probability Calculator

Calculate the probability of single and combined events.

Probability Calculator

Enter the probability of event A and event B (each between 0 and 1), then select Calculate.

P(A)

P(B)

How this is calculated

For two independent events A and B: P(A∩B) = P(A) × P(B) P(A∪B) = P(A) + P(B) − P(A∩B) Every other value shown — complements, "exactly one," "neither," and the two "one but not the other" cases — follows directly from these two.

Examples

If P(A) = 0.6 and P(B) = 0.3: P(A∩B) = 0.18 (both occur), P(A∪B) = 0.72 (at least one occurs), and P((A∪B)′) = 0.28 (neither occurs).

About this calculation

This assumes A and B are independent events — the outcome of one doesn't affect the probability of the other. Each probability must be between 0 (impossible) and 1 (certain).

Related tools

More calculators are on the way — browse everything planned on the Home page.

Frequently asked questions

What does "independent events" mean?

Two events are independent when one occurring doesn't change the probability of the other — for example, two separate coin flips. If your events depend on each other, these formulas don't apply.

Why does the calculator say my input is invalid?

Each probability must be a number between 0 and 1 (for example, 0.5 for a 50% chance) — not empty, not a percentage over 1, and not negative.