Complement Probability Calculator Formula

Understand the math behind the complement probability calculator. Each variable explained with a worked example.

Use the Complement Probability Calculator

Formulas Used

P(Not Event)

p_complement = 1 - p_event

Complement (%)

p_complement_pct = (1 - p_event) * 100

Odds Against

odds_against = (1 - p_event) / p_event

Variables

VariableDescriptionDefault
p_eventP(Event)0.35

How It Works

How to Calculate Complement Probability

Formula

P(A') = 1 - P(A)

The complement of an event A includes all outcomes where A does not happen. Since all probabilities must sum to 1, the complement is simply 1 minus the event probability. This is often useful for "at least one" problems where computing the direct probability is complex.

Worked Example

The probability of rain is 0.35. What is the probability it does not rain?

p_event = 0.35
  1. 01P(rain) = 0.35
  2. 02P(no rain) = 1 - 0.35 = 0.65
  3. 03As a percentage: 65%
  4. 04Odds against rain: 0.65 / 0.35 ≈ 1.857

Ready to run the numbers?

Open Complement Probability Calculator