MATH

Probability Calculator

Calculate probability using probability of a: p, probability of b: p, probability of a not occuring: p

Choose a probability modelProbabilities are entered as decimals from 0 to 1.

5 options

Probability of A: P(A)

Probability of B: P(B)

PROBABILITY0.2

Probability of Two Events: Calculates two-event relationships, solves independent-event probabilities from any two known values, evaluates repeated independent events or exact binomial successes, and finds normal-distribution interval probability.

Probability of A: P(A): 0.4
Probability of B: P(B): 0.5
Probability of A NOT occurring: P(A′): 0.6
Probability of B NOT occurring: P(B′): 0.5
Probability of A and B both occurring: P(A∩B): 0.2
Probability that A or B or both occur: P(A∪B): 0.7
Probability that A or B occurs but not both: P(A△B): 0.5
Probability of neither A nor B occurring: 0.3

Estimate based on the values shown

MethodCalculates two-event relationships, solves independent-event probabilities from any two known values, evaluates repeated independent events or exact binomial successes, and finds normal-distribution interval probability.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

EDITORIAL NOTES

Using the Probability Calculator responsibly

Page-specific guidance based on this calculator’s implemented method, inputs, and known limits.

What this result is useful for

The probability workspace covers several common event relationships. The important first step is identifying whether events are independent, mutually exclusive, conditional, or complements; those descriptions determine which equation applies.

Assumptions and limits

Inputs must represent valid probabilities and the chosen relationship must match the real process. Independence and equal likelihood are not automatic. A mathematically valid result can still be misleading when the model omits selection effects or changing conditions.

How to check the result

Every final probability should lie from zero to one, or zero to one hundred percent. Test boundary cases such as an impossible event and a certain event, then restate the result in plain language to confirm that the event and denominator are correct.

INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →

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