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Complementary Probability Calculator

Work out complementary probability instantly with clear inputs, formula shown and shareable results.

About Complementary Probability Calculator

The complement rule says P(not A) = 1 − P(A). Over independent trials the chance of no occurrence is qⁿ, so the chance of at least one is 1 − qⁿ — usually far easier than summing the cases directly.

Formulas

Complement rule

P(not A) = 1 − P(A)

At least once

P(at least one in n trials) = 1 − (1 − p)ⁿ

Worked example

With the default values below, Complementary Probability Calculator returns Probability it does not happen of 0.65000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Probability of the eventaccepts 0–100 %
35 %
Number of independent trialsminimum 1
5

Results

Probability it does not happen
0.65000000
As a percentage
65.0000 %
Probability it never happens in the trials
0.11602906
Probability it happens at least once
0.88397094

Step by step

  1. 1Values used
  2. 2Complement rule
  3. 3At least once
  4. 4Probability it does not happen= 0.65000000
  5. 5As a percentage= 65.0000 %
  6. 6Probability it never happens in the trials= 0.11602906
  7. 7Probability it happens at least once= 0.88397094

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

For a 35% event over 5 trials?

The complement is 65%, so it never happens with probability 0.65⁵ ≈ 0.1160 and happens at least once with probability 0.8840.

Why use the complement?

Computing 'at least one' directly means summing many cases; one minus 'none' is a single calculation.

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