PROB in WPS Spreadsheet: Sum Probabilities Within Bounds
Calculate interval probabilities from a complete discrete distribution with positive weights, explicit bounds and independently checked totals.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
PROB adds the probabilities assigned to outcomes within specified bounds. It operates on a discrete distribution: the supplied probabilities are weights attached to outcome values, rather than counts of observations or heights of a continuous probability density.
Syntax and supported examples
=PROB(x_range, prob_range, lower_limit, upper_limit)
The WPS text describes an optional upper limit, but all examples here supply both bounds explicitly. The original data use equal-sized numeric ranges, strictly positive probabilities and a total of exactly one. Zero-probability inputs, totals below one and omitted-upper behavior are outside these controls.
The vendor walkthrough uses outcomes 2, 7, 8, 1 with respective probabilities 0.1, 0.2, 0.3, 0.4. Its formula with bounds 2 and 7 returns 0.3. This includes both endpoint outcomes and corroborates the inclusive interval interpretation used below.
Enter a complete original distribution
| Row | A: outcome | B: probability |
|---|---|---|
| 2 | 1 | 0.125 |
| 3 | 3 | 0.25 |
| 4 | 5 | 0.375 |
| 5 | 7 | 0.25 |
- Check the weights: 1/8 + 2/8 + 3/8 + 2/8 = 1. Every weight is positive.
- Enter
=PROB(A2:A5,B2:B5,3,5)in D2. - Outcomes 3 and 5 meet the bounds. Add their weights, 2/8 + 3/8, to obtain 0.625.
- If displaying the result as a percentage, 0.625 corresponds to 62.5%; do not multiply it by 100 and then also apply percentage formatting.
The probabilities were chosen as binary-exact fractions, avoiding a rounded total such as 0.999 from imprecisely specified inputs. They are hypothetical model inputs, not measured probabilities of any real event.
Independent interval controls
All formulas use the unchanged A2:A5 and B2:B5 ranges.
| Lower | Upper | Selected outcomes | Expected probability |
|---|---|---|---|
| 3 | 5 | 3 and 5 | 0.625 |
| 1 | 7 | All four | 1 |
| 3 | 3 | 3 | 0.25 |
| 2 | 6 | 3 and 5 | 0.625 |
| 8 | 9 | None | 0 |
| 1 | 1 | 1 | 0.125 |
A result of zero for an interval containing no outcome is different from supplying a zero probability as an input. This guide does not infer acceptance of zero input weights from that empty-event result.
Practical checks before using a model
Keep each outcome beside its probability. Sorting one column alone assigns the weights to different events. Check the full distribution’s total separately with SUM; a formula returning a number is not proof that the model is complete or statistically justified.
For this complete original distribution, outcomes outside 3 through 5 carry 0.125 + 0.25 = 0.375, and 0.625 + 0.375 = 1. This complement calculation depends on the independently verified total of one. It does not assert how WPS validates an incomplete input distribution.
The lesson’s error remarks discuss probabilities outside its stated range, totals above one and mismatched counts. They do not resolve every boundary, including sums below one. No invalid-input error is asserted as an executed result here. Retain explicit positive weights and matching ranges when reproducing these controls. Compare with COUNT when the task concerns raw observations rather than assigned probabilities.
Availability and evidence scope
The official WPS lesson is dated 2019-06-25. The lesson leaves its applicability edition and platform unspecified; links elsewhere on the website do not establish a supported platform. A numeric build is not specified. The lesson date is a documented-by date, not a first-release date. First introduction, last functioning version and retirement or deprecation history remain unestablished. No cross-platform parity is inferred.
The complete lesson and its formula images or walkthrough were inspected on October 18, 2026. Original examples in this guide were independently calculated from the documented model; they were not executed in WPS or another spreadsheet engine. Historical vendor demonstrations are identified separately. Numeric approximations below are independent expectations, not promises about WPS display precision.