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Probability Calculator

Calculate event probability, complements, repeated trials, or the union and intersection of independent events.

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Complete guide

Probability calculator for outcomes, repeated trials and independent events

Use counts for an equally likely sample space or enter two known independent probabilities. Calculator24 returns the event, complement, repeated-trial or intersection and union probabilities with percentages and odds.

Editorial checkComplement, multiplication and independent-union formulas checked against OpenStax probability definitions.Updated September 10, 2026
Probability divides the sample spaceA valid probability ranges from zero to one. Its complement fills the remainder to one.1Event E2Complement E′3Whole sample space
Probability divides the sample spaceA valid probability ranges from zero to one. Its complement fills the remainder to one.

Probability from equally likely outcomes

Count the outcomes that satisfy the event and divide by all possible equally likely outcomes. The favorable count cannot exceed the total.

P(E)=n(E)÷n(S)

Complement probability

The complement contains every outcome outside the event. Event and complement probabilities always sum to one.

P(E′)=1−P(E)

Repeated independent trials

For at least one success, first calculate the chance of no successes and subtract it from one.

P(at least one)=1−(1−p)^n

Two independent events

Independence means learning whether A occurred does not change the probability of B. Multiply for both events and subtract the overlap when finding either event.

P(A∩B)=P(A)P(B)P(A∪B)=P(A)+P(B)−P(A∩B)

Worked die example

One specified face among six equally likely faces gives p=1/6. Three independent rolls have no-six probability (5/6)³, so at least one six is about 42.13%.

Assumptions and misuse

Replacement often supports independence; drawing without replacement usually does not. A mathematical result is only as reliable as its sample-space and independence assumptions.

Probability scale

Probabilities may be written as decimals, percentages or odds.
ProbabilityInterpretationComplement
0Impossible in the model1
0.25One in four0.75
0.5Even chance0.5
1Certain in the model0

Frequently asked questions

What is a favorable outcome?

An outcome included in the event being measured.

Can probability exceed 100%?

No. A valid probability is between 0 and 1, or 0% and 100%.

What does at least one mean?

One or more successes across the entered trials.

Why use the complement rule?

It often replaces many separate success cases with one no-success calculation.

Are mutually exclusive events independent?

Usually no. If one nonzero event occurs, the other cannot occur.

Does this predict real outcomes?

No. It evaluates the assumptions and probabilities entered.

What to keep in mind

The outcome model assumes outcomes are equally likely and trials are independent. Real-world dependence, biased sampling, changing conditions and uncertain input probabilities require a different model.

Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.

Sources and references

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