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Probability Calculator

Single and combined event probability, odds and repeated trials.

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Single event

—

As a decimal—
As a fraction—
Odds in favour—
Probability it does not happen—

Two events

Both happen — P(A and B)—
Either happens — P(A or B)—
Neither happens—
Exactly one happens—
P(A given B)—

Repeated trials

The chance of something happening at least once across many attempts.

—At least once
—Never happens
—Expected occurrences

Quick Tool Overview

The Probability Calculator works out the chance of a single event from favourable and total outcomes, then combines two events with AND, OR and NOT — including the case where they are not independent. Results come as a decimal, a percentage, a fraction and as odds.

What it does
Calculates single, combined and repeated-trial probabilities
You give it
Outcome counts or probabilities, and a number of trials
You get back
The probability as a decimal, percentage, fraction and odds
Best for
Statistics coursework, games, risk estimates and betting odds
Calculators Free, unlimited use No sign-up Runs in your browser

About the Probability Calculator

Work out the probability of a single event from favourable and total outcomes, then combine two events with AND, OR and NOT, including the case where they are not independent. Results are given as a decimal, a percentage, a fraction and as odds.

A repeated-trials panel answers the question people actually ask, which is the chance of something happening at least once across many attempts. That is calculated as one minus the probability of it never happening, and the result is frequently counterintuitive: an event with a one in a hundred chance occurs at least once in a hundred attempts about 63 percent of the time, not with certainty.

Key features of the Probability Calculator

Four representations

Decimal, percentage, fraction and odds are all given, so the answer fits whatever form the question used.

AND, OR and NOT

Two events can be combined every way, including when they are not independent.

At least once across many trials

Calculated as one minus the probability of it never happening, which is the question people actually ask.

Counterintuitive results made plain

A one-in-a-hundred event occurs at least once in a hundred attempts about 63 percent of the time, not with certainty.

Works from counts or probabilities

Enter favourable and total outcomes, or a probability directly — whichever you have.

How to use the Probability Calculator

  1. 1

    Enter a single probability

    Give favourable outcomes over total outcomes, or type a probability directly as a percentage.

  2. 2

    Combine two events

    Set the probability of each and choose whether you want both, either, or neither.

  3. 3

    Repeat the trial

    Enter a number of attempts to get the chance of at least one success across all of them.

Frequently asked questions

For independent events, multiply their probabilities. Two fair coin flips both landing heads is 0.5 x 0.5, which is 0.25 or 25 percent.

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