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Calculator Answers

Probability Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

A probability calculator computes the likelihood of events occurring based on probability theory. It determines single-event probability, its complement, and the joint probability of independent events (both A and B, or A or B). Additionally, it calculates the probability of achieving at least one success across multiple trials using binomial distribution math. Students, statisticians, and risk analysts use this tool to evaluate experimental outcomes, assess financial risks, and check homework solutions without performing manual fraction conversions.

Pick a mode (single event, complement, AND, OR, or 'at least one'). Enter the probabilities between 0 and 1. The calculator returns the result as a decimal, as a percent, and as a worked formula.

Quick Answer

Calculate probability metrics for single and multiple events. Enter your event counts or individual probabilities to see the likelihood of outcomes.

What to compute

Between 0 and 1. For 25% enter 0.25.

Notes

  • The AND and OR forms assume A and B are independent events.
  • If A and B are mutually exclusive, P(A or B) = P(A) + P(B). This calculator's OR uses the independence inclusion-exclusion form.
  • For full binomial probability (exactly k successes in n trials), use the binomial probability calculator.
Probability

Probability

0.5

50%

Decimal0.5
Percent50%
FormulaP(A) = 0.5

Probability is a number between 0 (impossible) and 1 (certain). Percent = decimal × 100. The complement is always 1 minus the original probability.

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Examples

Complement: P(A) = 0.4

1 − 0.4 = 0.6 (60%)

AND: 0.5 × 0.25

= 0.125 (12.5%)

OR: 0.5 + 0.25 − 0.125

= 0.625 (62.5%)

At least one success: p = 0.1, n = 10

1 − 0.9^10 ≈ 0.6513 (65.13%)

How it works

Each formula assumes the events behave as described (independence for AND/OR, identical-and-independent trials for at-least-one).

Complement · P(not A) = 1 − P(A)

Independent AND · P(A and B) = P(A) · P(B)

Independent OR · P(A or B) = P(A) + P(B) − P(A) · P(B)

At least one in n · 1 − (1 − p)ⁿ

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Frequently asked questions

As decimals between 0 and 1. For a 25% chance, enter 0.25. For a 70% chance, enter 0.7. The calculator displays both the decimal and the percent in the result.

The complement of A is 'not A', and its probability is 1 − P(A). For example, if the chance of rain is 0.4, the chance of no rain is 0.6.

Only when A and B are independent (one event does not affect the other). The calculator's AND mode assumes independence. If the events are not independent, you need conditional probabilities and the formula becomes P(A) · P(B|A).

For mutually exclusive A and B, P(A or B) = P(A) + P(B). For independent (but not necessarily exclusive) events, you must subtract the overlap: P(A or B) = P(A) + P(B) − P(A) · P(B). This calculator uses the independent form.

If a single trial has probability p of success, and you repeat the trial n independent times, the chance of at least one success is 1 − (1 − p)^n. This is the basic formula behind many practical probability questions.

Binomial probability (exactly k successes in n trials) is a separate page. This calculator covers the simpler everyday cases. For binomial, use the binomial probability calculator.