Formula and example
How it is calculated
P(X=k)=C(K,k)·C(N−K,n−k)/C(N,n). For at least k, sum the valid probabilities from k upwards.
Worked example
You know 10 of 20 topics and draw two. The chance of at least one known topic is 1−C(10,2)/C(20,2)=29/38≈76.3158%.
Things to check
- Every selection is equally likely and drawn topics are not returned.
- Knowledge is modelled as known or unknown. Partial knowledge and answer grading are not included.
Frequently asked questions
Why can I not simply add 50% twice?
The first draw changes the composition of the remaining topics. The cases in which both topics are known also overlap.