How this calculation works
Trial counts are whole numbers, so the real-valued threshold must be rounded upward to reach the target.
THE FORMULA
n ≥ ln(1−target)/ln(1−p)A worked example
At p = 0.2, ten trials give about 89.26% and eleven give about 91.41%.
Good to know
A certainty target requires certain success per trial.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Solve for the smallest number of independent trials required to meet a chance target.
The primary result is labeled “Minimum whole trials”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A certainty target requires certain success per trial.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
At p = 0.2, ten trials give about 89.26% and eleven give about 91.41%.
Which rule does this calculator apply?
n ≥ ln(1−target)/ln(1−p)