How this calculation works
Find the probability of k failures before the rth success and its cumulative probability.
THE FORMULA
P(X=k)=C(k+r−1,k)pʳ(1−p)ᵏA worked example
At p=1/2, two failures before the third success have probability 6/32.
Good to know
Trials must be independent and p must be positive.
Reference: OpenStax Introductory Statistics (opens in a new tab) ↗
Read the result
Find the probability of k failures before the rth success and its cumulative probability.
The primary result is labeled “Exact probability”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
Trials must be independent and p must be positive.
For a related exercise, try the statistics calculator.
A few questions, answered
How can I check the default inputs by hand?
At p=1/2, two failures before the third success have probability 6/32.
Which rule does this calculator apply?
P(X=k)=C(k+r−1,k)pʳ(1−p)ᵏ