How this calculation works
The complementary event requires every trial to fail. Independence allows their failure probabilities to be multiplied.
THE FORMULA
1 − (1−p)ⁿA worked example
With three trials at p = 0.2, no successes has probability 0.512, leaving 0.488.
Good to know
Trials must be independent with the same success probability.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Use the complement to find the chance of one or more successes.
The primary result is labeled “Probability of at least one”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Trials must be independent with the same success probability.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
With three trials at p = 0.2, no successes has probability 0.512, leaving 0.488.
Which rule does this calculator apply?
1 − (1−p)ⁿ