Probability of At Least One Calculator
Enter the chance per try and the number of tries.
Your numbers
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Your results
Probability of at least one success
Probability of at least one success
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Probability of none
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Tries needed for the target probability
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Expected successes
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Probability of At Least One Calculator by TheCalcTools
How the Probability of At Least One Calculator works
It is easier to calculate the chance of no success: (1 − p)ⁿ for independent tries. The chance of at least one is 1 minus that.
Solving 1 − (1 − p)ⁿ ≥ target gives the number of tries needed: n = ln(1 − target) ÷ ln(1 − p), rounded up.
The formula
P(at least one) = 1 − (1 − p)ⁿ
Worked example
Using the default values shown in the calculator:
| Chance of success on each try | 5 % |
|---|---|
| Number of tries | 20 |
| Target probability (for tries needed) | 90 % |
- A 5% chance tried 20 times: 64.15% for at least one success.
- For 90% you need 45 tries.
Result:
| Probability of at least one success | 64.15% |
|---|---|
| Probability of none | 35.85% |
| Tries needed for the target probability | 45 |
| Expected successes | 1.00 |
Frequently asked questions
If something has a 1 in 20 chance, will it happen in 20 tries?
Not certainly: the chance is about 64%. You need 45 tries for 90%.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.