Probability Calculator

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Calculate the probability of two events occurring together or separately, and the binomial chance of exactly k successes in n trials. Free, instant and easy to read.

Two events

Enter a percentage (e.g. 50) or a decimal between 0 and 1.

Binomial — exactly k successes

P(A and B) –
P(A or B) –
P(not A) –
P(exactly k) –
Independent events assume one outcome does not affect the other. Mutually exclusive events cannot both happen, so P(A and B) is 0. The binomial result is the chance of exactly k successes in n independent trials.

About Probability Calculator

The probability calculator handles two classic setups. For two events A and B, enter P(A) and P(B) — as percentages or decimals — and it returns P(A and B), P(A or B) and P(not A), under your choice of independent or mutually exclusive events.

The distinction drives the math: independent events multiply, so P(A and B) = P(A) × P(B), while mutually exclusive events cannot co-occur, making P(A and B) zero and P(A or B) a simple sum. The general addition rule P(A or B) = P(A) + P(B) − P(A and B) ties it together.

A separate binomial section computes the chance of exactly k successes in n independent trials with success probability p — the “exactly 3 heads in 10 flips” kind of question — free and instant.

How to use Probability Calculator

  1. Enter P(A) and P(B) as percentages (e.g. 50) or decimals between 0 and 1.
  2. Choose whether the events are independent or mutually exclusive.
  3. Read P(A and B), P(A or B) and P(not A).
  4. For binomial problems, enter the trials n, successes k and success probability, then read P(exactly k).

Frequently asked questions

One outcome does not affect the other — like two separate coin flips. Under independence, the joint probability is the product: P(A and B) = P(A) × P(B).

Events that cannot both happen, like rolling a 3 and a 5 on one die roll. Their joint probability is zero, so P(A or B) reduces to P(A) + P(B).

Yes — type 50 for a coin flip or 0.5 as a decimal; the calculator accepts either form and treats them identically.

With the binomial formula: P(exactly k) = nCk × pᵏ × (1−p)ⁿ⁻ᵏ, the chance of exactly k successes in n independent trials that each succeed with probability p.

Enter n = 10, k = 3 and success probability 0.5 in the binomial section — the result is about 11.7%. Note this is “exactly 3”, not “3 or more”.
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