Probability Calculator

Calculate single-event, union, intersection, complement, and repeated-event probabilities.

Enter your values

Change any field. The result is recalculated on this device.

Formula, example and assumptions
Probability0.125

Your result

Local calculation
Probability0.125

The result is the chance of the selected event, shown from 0 to 1 and as a percentage. Combined events and repeated trials use the stated independence assumption.

Probability operation
Independent A and B
Probability A (0 to 1)
0.5
Probability B (0 to 1)
0.25
See how this is calculated

Result breakdown

As a percentage
12.5%
Check the inputs and method

These are your current inputs, not the worked example further down the page.

Probability operation
Independent A and B
Probability A (0 to 1)
0.5
Probability B (0 to 1)
0.25

Method

Complement = 1 − p. Independent both = pq. Independent either (including both) = p + q − pq. At least once in n independent trials with unchanged probability p = 1 − (1 − p)ⁿ.

Read the worked example and assumptions

How this calculation works

Select whether you need a complement, two independent events together, either independent event, or at least one occurrence across repeated trials. Enter probabilities as fractions from 0 to 1. These formulas combine supplied probabilities; the calculator does not estimate them from observations.

Complement = 1 − p. Independent both = pq. Independent either (including both) = p + q − pq. At least once in n independent trials with unchanged probability p = 1 − (1 − p)ⁿ.

Worked example

This example uses illustrative inputs. Your current result is shown above.

For an event with p = 0.2 and three independent trials, no occurrence has probability 0.8³ = 0.512. At least once is 1 − 0.512 = 0.488, or 48.8%.

Assumptions and limits

  • Enter 0.2 for 20%, not 20.
  • The both/either modes assume independent events. Repeated trials also assume independence and the same p on each trial.
  • “Either” includes cases where both occur; this is not an exclusive-or calculation.

Questions people ask

Can I use these formulas for dependent events?

Not without adjustment. If one outcome changes the chance of another, the joint probability requires conditional information that these fields do not collect.

Is “at least once” the same as exactly once?

No. At least once includes one, two or more successes. It is calculated by subtracting the chance of zero successes from one.

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