Probability calculator
Chances of two events together, either one, or an event repeated.
About this calculator
This probability calculator works out the chances of two independent events: both happening, either one, exactly one or neither.
It also handles repeated tries, such as rolling a die or entering a draw many times, with the chance of at least one success and of an exact number of successes.
How it works
For independent events, P(A and B) = P(A) × P(B) and P(A or B) = P(A) + P(B) − P(A and B). For repeats, the chance of at least one success is 1 − (1 − p)ⁿ.
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Worked example
- Work out: Two independent events
- Probability of A: 50%
- Probability of B: 30%
Both A and B: 15%
Common questions
What does independent mean in probability?
Two events are independent if one happening doesn't change the chance of the other, like two separate coin flips. These formulas assume independence.
What is the chance of rolling a six at least once in six rolls?
1 − (5/6)⁶, which is about 66.5%, not 100%. Enter 16.67% and 6 tries to check.
How do I turn odds into a probability?
Odds of 3 to 1 against mean 1 success for every 4 tries, a probability of 1 ÷ 4 = 25%.
The story behind it
Where the idea came from: Probability theory began with letters between Blaise Pascal and Pierre de Fermat in 1654, about how to split the stakes of an unfinished game.
A gambler asked Pascal how to share the prize fairly when a game was stopped early. Pascal and Fermat's answer laid the foundations of probability. The same reasoning now runs through insurance, medicine, weather forecasts and games.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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