Probability Calculator
Work out probabilities for independent events. Find the chance that both events happen, at least one, or neither, or the chance that something happens at least once when you try several times.
Both A and B
15%
Check the highlighted fields to see your result.
- A or B (at least one)
- 65%
- Neither
- 35%
- Only one of them
- 50%
Results are estimates for information only and do not constitute financial, medical, or legal advice.
How it works
For independent events, you multiply probabilities to find the chance that both happen. To find the chance that something happens at least once in several tries, it's easier to work out the chance it never happens and subtract that from 100%.
The formulas
P(A and B) = P(A) × P(B)
P(A or B) = P(A) + P(B) − P(A) × P(B)
P(at least once in n tries) = 1 − (1 − p)n
Worked example
What's the chance of rolling at least one 6 in 4 rolls of a die?
- The chance of not rolling a 6 in one roll is 5/6.
- The chance of no 6 in 4 rolls: (5/6)⁴ ≈ 0.4823.
- At least one 6: 1 − 0.4823 ≈ 51.77%.
Frequently asked questions
What does "independent" mean?
Two events are independent when one happening doesn't change the chance of the other. Two coin flips are independent. Drawing two cards from the same deck without putting the first one back is not, so these formulas don't apply there.
If something has a 1 in 6 chance, will it happen in 6 tries?
Not for sure. The chance of rolling at least one 6 in 6 tries is about 66.5%, not 100%. Each try is a new chance, and past results do not make a 6 "due." This is a common mistake known as the gambler's fallacy.
How do I convert odds to a percentage?
A chance of 1 in 4 is 1 ÷ 4 = 0.25, or 25%. Odds of 1 to 3 (one way to win, three ways to lose) are the same: 1 ÷ (1 + 3) = 25%.