What is the complement rule in probability?

The complement rule states that the probability of an event NOT occurring equals 1 minus the probability that it does occur: P(A') = 1 - P(A). Since all probabilities must sum to 1, the event and its complement are mutually exclusive and exhaustive.

Can I enter a probability as a fraction?

Yes. Enter values like 1/6, 3/4, or 7/10 and the calculator will parse the fraction automatically. You can also enter decimals (0.25) or percentages (25%).

What if my probability is greater than 1 or less than 0?

Probabilities must be between 0 and 1 inclusive (or equivalently 0% to 100%). The calculator will show an error if you enter an out-of-range value.

What does the odds ratio mean?

The odds ratio expresses the probability as "X to Y" odds against the event occurring. For example, a 25% chance corresponds to 3 to 1 odds against (three chances of not occurring for every one chance of occurring).

How is this different from conditional probability?

The complement rule deals with a single event and its opposite. Conditional probability P(A|B) describes the probability of A given that B has already occurred — a different concept that requires two events.

Complement Probability Calculator

Calculate the probability that an event does NOT occur using the complement rule P(A') = 1 - P(A).

Event Probability

P(A) — Probability of the event

Enter as decimal (0.3), fraction (3/10), or percentage (30%)

Quick Examples

Result

Enter a probability above to see the complement.

Summary

The Complement Probability Calculator applies the fundamental complement rule of probability theory: P(A') = 1 - P(A). Enter the probability of any event — as a decimal, fraction, or percentage — and instantly see the probability of that event not happening. This tool is useful for students, statisticians, and anyone working with basic probability problems.

How it works

Enter the probability of your event in decimal (0.3), fraction (3/10), or percentage (30%) format.
The calculator parses your input and converts it to a decimal between 0 and 1.
It applies the complement rule: P(A') = 1 - P(A).
Results are displayed as a decimal, a percentage, and as an odds ratio.
Use the swap button to flip the event and its complement.

Use cases

Find the probability of NOT rolling a specific number on a die.
Calculate the chance a product does NOT fail given its failure rate.
Determine the probability of missing a target given a hit rate.
Quickly verify complement values in homework or exam problems.
Convert between event probability and its complement for decision analysis.
Understand risk in terms of the probability that something will not happen.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu