HYPGEOM.DIST in Collabora Office: Model Finite Sampling Without Replacement
Use Collabora HYPGEOM.DIST for finite-population sample counts, reproduce combinatorial probabilities, and distinguish it from independent trials.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =HYPGEOM.DIST(2;3;4;10;0) has independently expected result 0.3. It is the probability of selecting exactly two marked items when drawing three without replacement from ten items, four of which are marked.
Syntax and finite-population model
=HYPGEOM.DIST(X; NSample; Successes; NPopulation; Cumulative)
X is the marked-item count in the sample. NSample is the sample size. Successes is the marked-item count in the entire population, and NPopulation is the total population size. Cumulative=0 or FALSE selects an exact-count probability; the dedicated help says other values or TRUE select the cumulative probability. Use explicit zero or one.
All four counts should be integers. For these examples require NPopulation>0, 0<=Successes<=NPopulation and 0<=NSample<=NPopulation. The sample is chosen uniformly without replacement. The word “success” is just a label for the counted category; it need not describe a beneficial outcome.
Possible X values run from MAX(0;NSample-(NPopulation-Successes)) through MIN(NSample;Successes). This lower bound matters when the sample is too large to avoid marked items.
Example 1: reproduce an exact probability
Imagine ten labeled items, with four marked and six unmarked. Draw three. There are COMBIN(10;3)=120 equally likely unordered samples.
Exactly two marked items can be chosen in COMBIN(4;2)=6 ways, and the one unmarked item in COMBIN(6;1)=6 ways. Thus the desired probability is 6*6/120=0.3.
Put X=2, NSample=3, Successes=4 and NPopulation=10 in B2:B5. Use =HYPGEOM.DIST(B2;B3;B4;B5;0) in B7. A transparent reference expression is =COMBIN(B4;B2)*COMBIN(B5-B4;B3-B2)/COMBIN(B5;B3) for these valid integer inputs.
Example 2: build the complete sample-count distribution
Put 0, 1, 2, 3 in A10:A13. Use =HYPGEOM.DIST(A10;3;4;10;0) in B10 and fill down. Independent probability targets are 1/6, 1/2, 3/10 and 1/30, approximately 0.166666667, 0.5, 0.3 and 0.033333333.
These exhaust the possible outcomes and sum to one. Their cumulative targets in the same order are approximately 0.166666667, 0.666666667, 0.966666667 and 1, obtained with a final argument of one.
The expected marked-item count is NSample*Successes/NPopulation=1.2. Multiplying each A value by its B probability and summing gives the same expectation. An expectation need not itself be an attainable integer outcome.
Advanced application: form the correct upper tail
“At least two marked items” has probability =1-HYPGEOM.DIST(1;3;4;10;1), independently 1/3. Subtract through one, because the desired event includes two.
“More than two” is instead =1-HYPGEOM.DIST(2;3;4;10;1), independently 1/30. Writing the event in words beside the formula helps prevent a one-count threshold error.
Advanced application: compare with replacement
If each draw independently sampled a marked item with probability 0.4, the binomial probability of exactly two marked items in three draws would be 0.288. The without-replacement hypergeometric result is 0.3.
After a marked item is removed, the next marked-item probability changes. That dependence is the reason not to substitute a fixed-probability binomial model automatically. For a very small sample relative to a large population the models can be close, but the sampling design determines which is appropriate.
The official example with population 100, marked count 90 and sample size two gives exact-two probability 0.809090909 and cumulative-through-two probability 1. Interpret it as finite sampling without replacement; repeated independent physical trials would be a different model.
Errors and troubleshooting
Validate whole-number counts and population consistency. The support formula identifies feasible exact counts, but this guide does not certify native handling of every out-of-support, fractional or invalid argument. The brief documentation does not enumerate those error codes.
Check argument order carefully: sample size and population marked count occupy different positions. Do not let a filtered worksheet hide the fact that the population totals changed. The function calculates a probability from the counts supplied; it does not ensure the sample was random or drawn without replacement.
Availability and verification
The exact function is documented in Collabora Office 26.04 desktop help. Its source snapshot was retrieved on 2026-10-13 and hash-verified for this guide on October 15, 2026. Desktop documentation is not proof of Online or mobile support.
First introduced release and last functioning version are unknown. The available dedicated source does not establish those releases. No native Collabora or WPS run occurred. Numerical values are independent mathematical expectations, not certification of application-specific errors, numerical tolerances or all edge cases. Formulas use English names and semicolon separators.
The help identifies the namespace COM.MICROSOFT.HYPGEOM.DIST and says this function is outside the cited OpenFormula 1.3 standard. This format disclosure does not prove identical behavior in another product. Keep exact dotted names when checking imported workbooks.