Probability Calculator

Calculate complements, intersection and union for two independent events

A and B are treated as independent events.

Your result will appear here.

About the Probability Calculator

Probability measures how likely an event is on a scale from 0 to 1, or 0% to 100%. This calculator handles common single-event, combined-event and complementary probability relationships.

The arithmetic only works when the event structure is described correctly. Independent events, mutually exclusive events and conditional events use different rules.

How to Use the Probability Calculator

  1. Choose the probability relationship that matches the problem.
  2. Enter event probabilities as decimals or percentages using the units shown.
  3. Confirm whether the events are independent or mutually exclusive before applying a combination rule.
  4. Calculate the result and check that the probability remains between 0 and 1.

How the Calculation Works

For independent events A and B occurring together, P(A and B) = P(A)×P(B). For mutually exclusive alternatives, P(A or B) = P(A)+P(B).

The complement is P(not A)=1−P(A). More general unions use P(A or B)=P(A)+P(B)−P(A and B) to avoid double-counting overlap.

Worked example

Probability Calculator Worked Example

Two independent coin flips

The probability of heads on one fair flip is 0.5. For heads on both independent flips, 0.5×0.5 = 0.25, or 25%.

Result guide

Understanding Your Probability Calculator Result

A probability is a model of uncertainty, not a guarantee about one outcome. A 25% event can occur on the next trial and a 90% event can fail.

Before you rely on the answer

Assumptions and Limitations

  • Input probabilities are valid values from 0 to 1 or 0% to 100%.
  • The selected independence or exclusivity assumption matches the events.
  • Probabilities are based on an appropriate model or data source.

Practical tip

Using This Result in Practice

Write the event in words before choosing a formula. P(A and B), P(A or B) and P(not A) often sound similar in conversation but require different arithmetic.

Related calculations

Useful Calculations to Continue With

If you are starting from odds rather than direct probabilities, use the Odds & Probability Calculator.

If the same independent trial is repeated many times and you need the probability of a specific number of successes, use the Binomial Probability Calculator.

Common questions

Probability Calculator FAQ

Can probability be greater than 100%?

No. A valid probability ranges from 0 to 1, equivalent to 0% to 100%.

When do I multiply probabilities?

For the probability that independent events all occur, multiply their probabilities.

What is a complementary probability?

It is the probability that an event does not occur: 1 minus the event probability.