Education
Probability Calculator
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.
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
0.5
50%
Probability is a number between 0 (impossible) and 1 (certain). Percent = decimal × 100. The complement is always 1 minus the original probability.
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
Related probability and stats calculators
- Binomial probability calculator for exactly-k, at-most-k, and at-least-k successes in n trials.
- Normal distribution calculator for tails and intervals on the bell curve.
- Poisson distribution calculator for event-rate problems.
- Permutation calculator for ordered arrangements.
- Combination calculator for unordered selections.
- All education calculators.
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.
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