Probability Calculator
Work out probabilities for the situations that come up most often: one event from counted outcomes, two events that are independent or mutually exclusive, a conditional probability, Bayes’ theorem for test results, and the chance of exactly, at least or at most k successes in repeated trials. Probabilities can be typed as decimals, percentages or fractions, and exact fractions are kept wherever possible.
Calculate a Probability
Result
Formula and working
How to Use the Probability Calculator
- Choose the type of problem.
- Enter the counts or probabilities (for example 0.25, 25% or 1/4).
- Press Calculate and read the results with the formulas used.
About This Tool
Students in statistics and probability courses, board-game and card players, and anyone interpreting medical test accuracy or risk figures.
Input: Probabilities or counts · Output: Probability.
Features and Limitations
Features
- Five problem types in one place.
- Accepts decimals, percentages and fractions; results shown as fraction, decimal and percentage.
- P(and), P(or), P(exactly one), P(neither) and more for two events.
- Binomial exactly / at least / at most k for up to 100,000 trials.
Limitations
- Assumes outcomes are equally likely (single event) and trials are independent with a constant probability (binomial).
- Binomial results use floating point and are shown to 8 significant digits.
- Dependent events other than the conditional and Bayes modes need P(A and B) to be entered directly.
- Results are computed in your browser; nothing you enter is sent to a server.
Example
Rolling a 6 is 1/6 ≈ 16.67%. For independent events with P(A) = 1/2 and P(B) = 1/6: P(A and B) = 1/12 and P(A or B) = 7/12. A test with 95% sensitivity and a 5% false-positive rate for a 1% condition gives P(A | positive) = 19/118 ≈ 16.1%.
Frequently Asked Questions
What is the difference between independent and mutually exclusive?
Independent events do not affect each other (two coin flips), so P(A and B) = P(A) × P(B). Mutually exclusive events cannot happen together (rolling a 1 and a 6 on one die), so P(A and B) = 0.
How do I calculate the probability of at least one success?
Use the complement: 1 − P(no successes) = 1 − (1 − p)^n. The repeated-trials mode shows this directly.
Why is a positive test often less conclusive than it sounds?
When a condition is rare, false positives from the large healthy group can outnumber true positives. Bayes’ theorem combines the test accuracy with how common the condition is.
Can I enter probabilities as percentages?
Yes. 25%, 0.25 and 1/4 are all understood. Values must be between 0 and 1 (0% to 100%).
Related Tools
More like this: all Math tools, all Calculators tools or the TinySandy home page.