How it works
Independent trials with constant success probability have zero-success probability (1−p)^n; its complement is used. This form solves for probability of at least one success; enter the known quantities in Success probability per trial, Independent trial count.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Success probability per trial | 10 % | Formula symbol: p. Enter the percentage as a number: for 15%, enter 15. Use a non-negative value. Allowed range: 0–100. |
| Independent trial count | 10 | Formula symbol: n. Enter a numeric value. Use a whole number. Use a non-negative value. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Success probability per trial
- 10 %
- Independent trial count
- 10
Complete example results
- Probability of at least one success
- 65.13215599 %
Reading the result
The result solves for probability of at least one success from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the probability of at least one success result?
Trials must be independent. A target probability does not guarantee an outcome. Required trials round up; a 100% target and singular inverse boundaries do not give a finite count.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: ocw.mit.edu