Probability Calculator
- A and B
- A or B
- Not A
- Not B
- Exactly one of A, B
- Neither A nor B
At least once in n trials
- Exactly one success
How to use
- Enter P(A) and P(B) as percentages, for example 30 for 30%.
- Read the six combined probabilities for independent events.
- For repeated tries, enter the chance of one success and the number of trials to get the chance of at least one.
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).
Exactly one happens: P(A)(1 − P(B)) + P(B)(1 − P(A)). Neither happens: (1 − P(A))(1 − P(B)).
At least once in n trials: 1 − (1 − p)^n. A 5% chance repeated 20 times gives 64.2%, not 100%.
FAQ
What does independent mean?
One event happening does not change the chance of the other. Two separate coin flips are independent. Drawing two cards from one deck without replacement is not.
Can I use fractions or decimals?
Enter percentages from 0 to 100. For 1/6, type 16.667. Results are shown both as percentages and as decimals.
Why is "at least once" not just p times n?
Chances do not add up past 100%. Two 50% tries do not make a sure thing. The tool takes the complement: the chance that every try fails, subtracted from 1.