HYPGEOMDIST in WPS Spreadsheet: Sampling Without Replacement

=HYPGEOMDIST(sample_s, number_sample, population_s, number_population)

Sample_s is the desired success count in the sample. Number_sample is the sample size. Population_s is the total number of success items in the population, and number_population is its total size. All original examples use valid small integer counts.

For x successes in a sample of n, from M successes among N population items, the documented formula is C(M,x)*C(N−M,n−x)/C(N,n). The first combination selects successes; the second selects failures; the denominator counts all possible samples.

A hypothetical population contains ten items, four marked as successes and six as failures. Draw three items without replacement. Find the probability of exactly one success.

1. Put 1, 3, 4, 10 in B1:B4 in that order.
2. Use =HYPGEOMDIST(B1,B2,B3,B4) in B6.
3. Count favorable subsets: C(4, 1)C(6, 2)=415=60.
4. Count all three-item subsets: C(10, 3)=120.
5. The independent expected probability is 60/120=0.5.

The result concerns exactly one success. It is not automatically the probability of one or fewer successes.

The first four rows exhaust all possible success counts in the original three-item sample. Their probabilities sum to 1. In particular, the probability of at least two successes is 3/10+1/30=1/3. This cumulative result is an independent sum; the documented four-argument signature itself returns a point probability.

With replacement and independent draws, success probability would stay 4/10 at every draw. The probability of exactly one success in three such draws would be 30.40.6^2=0.432, rather than 0.5. Neither result is universally preferable: they answer different sampling designs.

For the without-replacement design, a useful arithmetic check is the expected number of successes nM/N=34/10=1.2. Weighting the four possible counts by their probabilities above gives the same mean. This expectation is not a promise about one sample.

The vendor example =HYPGEOMDIST(5,10,25,80) displays 0.112254757. Its formula image explicitly maps all four arguments to the combination expression, avoiding confusion between sample and population success counts.

The lesson discusses truncation and a list of invalid-input conditions. Original controls stay within valid integer combinations; they do not certify exact error behavior for malformed counts, impossible events or fractional arguments. No cumulative argument or modern dotted alias is imported. PROB is useful for summing an explicitly tabulated distribution, with its own validation requirements.

The official WPS lesson is dated 2019-06-19 and explicitly labels WPS Office for Windows Personal. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.

The complete lesson and its formula images and walkthrough were inspected on October 18, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.