How it works
For random draws without replacement, expected marked items equal draw count times the marked share of the finite population. This form solves for number of draws without replacement; enter the known quantities in Expected marked quantity, Marked population items, Total population.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Expected marked quantity | 4 | Formula symbol: expected. Enter a numeric value. Use a non-negative value. |
| Marked population items | 20 | Formula symbol: marked. Enter a numeric value. Use a whole number. Use a non-negative value. |
| Total population | 100 | Formula symbol: population. Enter a numeric value. Use a whole number. Must be greater than zero. |
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.
- Expected marked quantity
- 4
- Marked population items
- 20
- Total population
- 100
Complete example results
- Number of draws without replacement
- 20
Reading the result
The result solves for number of draws without replacement 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 number of draws without replacement result?
Expectation is neither a realised count nor a probability of a specific outcome. Inverse target counts round up to a minimum integer. Draws and marked items cannot exceed the population.
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: math.ucsd.edu