MATH

Probability Calculator

Estimate probability from probability of a p(a), probability of b p(b) with the Probability Calculator.

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.

CALCULATOR GUIDE

How to use the Probability Calculator

Estimate probability from probability of a p(a), probability of b p(b) with the Probability Calculator. It includes Probability of Two Events, Probability Solver for Two Events, Probability of a Series of Independent Events, Binomial exact successes, Probability of a Normal Distribution workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.

Step by step

For the Probability example, select Probability of Two Events and enter probability of a p(a), probability of b p(b). Keep each value in the unit displayed beside its field.
Review the selected Probability workflow and inputs, then read probability in the result panel.
Change one Probability assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.

How the calculation works

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.

Worked example

To reproduce the Probability worked example, reset the calculator. Select the Probability of Two Events workflow. Use probability of a p(a) 0.4; probability of b p(b) 0.5. The result is probability of 0.2. 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. Review the displayed units before comparing the result.

Understanding the result

The Probability reports probability. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.

How to check the answer

Check the Probability answer by substituting probability back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match 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.

Common questions

What does the Probability calculate?

Estimate probability from probability of a p(a), probability of b p(b) with the Probability Calculator.

Which inputs does the Probability example use?

The worked example uses probability of a p(a), probability of b p(b) in the Probability of Two Events workflow. Other workflows can show different fields. Keep the chosen workflow and units with the result when comparing calculations.

Is the Probability result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck probability of a p(a), probability of b p(b) and use probability only for a decision where that level of precision is appropriate.

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

KEEP GOING

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