How do I calculate the probability of two independent events both happening?

Multiply their individual probabilities. If P(A) is 0.5 and P(B) is 0.4, then P(A and B) = 0.5 × 0.4 = 0.2, or 20%.

How do I calculate the probability of either event happening?

Use P(A or B) = P(A) + P(B) − P(A and B). For independent events this is P(A) + P(B) − P(A)·P(B).

What is the complement of a probability?

The complement is the probability that the event does not happen, equal to 1 minus the probability of the event.

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Probability Calculator

Enter the probability of one or two events and read off the single-event odds and complement, plus the combined probabilities — A and B, A or B, neither, and exactly one. Everything updates as you type.

Probability of A %

Probability of B % — optional

Single event (A)

P(A)

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Complement P(not A)

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Odds for

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Odds against

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Two independent events (A & B)

P(A and B)

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P(A or B)

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P(neither)

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P(exactly one)

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The two-event results assume A and B are independent (one happening does not change the chance of the other).

How to calculate combined probabilities

Once you know the probability of each event (a number between 0 and 1, or 0–100%), the standard combinations follow from a few rules.

Both events (independent)

P(A and B) = P(A) × P(B)

At least one event

P(A or B) = P(A) + P(B) − P(A and B)

Neither event

P(neither) = (1 − P(A)) × (1 − P(B))

Exactly one event

P(exactly one) = P(A or B) − P(A and B)

Odds from a probability

Odds for an event compare the chance it happens to the chance it doesn't. If P(A) = 0.25, the odds for are 0.25 : 0.75 = 1 : 3, and the odds against are 3 : 1.

Frequently asked questions

How do I find the probability of two events both happening?

For independent events, multiply their probabilities. If P(A) = 0.5 and P(B) = 0.4, then P(A and B) = 0.2 (20%).

How do I find the probability of either event happening?

Use P(A or B) = P(A) + P(B) − P(A and B). Subtracting the overlap avoids counting it twice.

What does “independent” mean here?

Two events are independent when one occurring does not change the probability of the other. The two-event results on this page assume independence.

Do you store the numbers I enter?

No. The calculator runs entirely in your browser. Nothing you type is uploaded or saved.