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Probability Calculator

Calculate probabilities for events, unions, intersections, Bayes’ theorem, and repeated trials.

Updated

What is the Probability Calculator?

Use this probability calculator to solve common event-based probability problems in one place.

It supports single-event probability, two independent events, conditional probability, Bayes’ theorem, and the chance of at least one success across repeated trials.

The calculator is designed for fast, practical use. Enter decimal probabilities between 0 and 1, switch modes instantly, and see clean result tiles with complements, unions, intersections, and posterior values where relevant.

How it works

1. Choose a mode

Select the probability type you want to calculate: single event, two independent events, conditional probability, Bayes’ theorem, or at least once across repeated trials.

2. Enter the values

Fill in the probability inputs using decimals from 0 to 1. For repeated trials, enter a whole number greater than 0.

3. Review the result

The calculator validates your input and returns the correct formula output. Depending on the mode, you will see the event probability, complement, joint probability, union probability, posterior probability, or repeated-trial result.

4. Use the formulas

For two independent events, the calculator uses multiplication and addition rules. For conditional probability and Bayes-style problems, it applies the relevant probability relationships and shows the result instantly.

Examples

Single event probability

Find the probability of one event and its complement.

P(A) = 0.4
P(A) = 0.4000, complement = 0.6000

Two independent events

Calculate the joint and union probability of two independent events.

P(A) = 0.4, P(B) = 0.25
P(A∩B) = 0.1000, P(A∪B) = 0.5500

At least once across trials

Find the chance of success at least once across repeated independent trials.

p = 0.1, trials = 10
At least once = 0.6513

Frequently asked questions

What can this probability calculator solve?

It can solve single-event probability, two independent events, conditional probability, Bayes’ theorem style problems, and repeated-trial probabilities.

What number format should I use?

Use decimals between 0 and 1, such as 0.25 or 0.7. For trials, use a whole number like 5 or 10.

Does it support percentages?

The calculator works with decimal probabilities for accuracy and consistency. If you have a percentage, divide it by 100 before entering it.

What does the complement mean?

The complement is the probability that the event does not happen. If an event has probability 0.4, its complement is 0.6.

How do independent events work?

For independent events, the calculator multiplies probabilities to find the joint probability. It also calculates the union using the addition rule.

What if I enter an invalid value?

The calculator shows a clear error message if a value is missing, not numeric, outside 0 to 1, or if the number of trials is not a positive whole number.

Can I use this for Bayes’ theorem problems?

Yes. The calculator includes a Bayes-style mode for updating a prior probability using likelihood and false-positive rate inputs.

What is the repeated-trials mode for?

It calculates the chance of at least one success across multiple independent trials, which is useful for event likelihood, quality checks, and simple risk questions.

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