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Statistics & Probability

Verified calculator with a transparent formula

Statistics & Probability

Complementary Probability Calculator.

Calculates the probability that an event does NOT occur, given the probability that it does occur.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the probability of the event occurring as a percentage.

  2. 2

    Subtract that value from 100.

  3. 3

    The result is the probability that the event does not occur.

100 - event_probability

Frequently asked questions

What does complementary probability mean?

It is the probability that an event does not happen, equal to 1 minus the event probability.

Can I enter a probability greater than 100%?

No, probabilities must be between 0% and 100%.

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Results

Formula checked

Complementary probability

70%

Ask Anything

Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the probability that an event does NOT occur, given the probability that it does occur.

  1. Enter the probability of the event occurring as a percentage.
  2. Subtract that value from 100.
  3. The result is the probability that the event does not occur.

Formulas

The math behind this calculator, written out so you can verify the result.

Complementary rule

P(not A) = 1 - P(A)

The probability of the complement is one minus the probability of the event.

Example:

Input: P(A) = 0.30

Calculation: 1 - 0.30

Result: 0.70

Real-world use cases

Where this calculation shows up in everyday life.

Quality control

Estimate the chance a product is not defective given the defect rate.

Example: Defect rate 2% → 98% non-defective.

Risk assessment

Find the probability of no failure when failure probability is known.

Example: Failure 5% → 95% no failure.

Tips and common mistakes

Tips

  • Always express probabilities as percentages or decimals consistently.
  • The complement of an event includes all other possible outcomes.
  • Check that your input is between 0 and 100.

Common Mistakes to Avoid

  • Forgetting to subtract from 100 when using percentages.
  • Using decimals instead of percentages without converting.
  • Assuming complementary probability is the same as odds.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.