How it works
Find the probability of exactly k successes in independent trials sharing a fixed success probability between zero and one.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Trials | 10 | Enter a numeric value. Use a whole number. Must be greater than zero. Allowed range: 1–170. |
| Exact successes | 3 | Enter a numeric value. Use a whole number. Use a non-negative value. Allowed range: 0–170. |
| Success probability | 0.5 | Enter a numeric value. Use a non-negative value. Allowed range: 0–1. |
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.
- Trials
- 10
- Exact successes
- 3
- Success probability
- 0.5
Complete example results
- Result
- 0.1171875
Reading the result
Check the probability scale, sample size and assumptions stated by the method. A decimal probability of 0.5 represents 50%. Mean and spread inputs must describe the same dataset; the calculation does not validate those estimates.
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.
Is this the probability of at least k successes?
No. The result is P(X=k), the probability of exactly k successes. Enter 0.5 for a 50% success probability. With 10 trials and exactly 3 successes, p=0.5 gives 0.1171875, equivalent to 11.71875%. Trials must be independent with the same success probability.
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.