PROB in Excel: Discrete Probability Tables and Explicit Interval Limits
Calculate Excel interval probabilities from an aligned discrete distribution, validate probability weights and distinguish a point probability from an expected value.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: PROB(x_range,prob_range,[lower_limit],[upper_limit]) adds probabilities for a specified event in a discrete table. Omitting the upper limit requests equality with the lower limit, rather than an open-ended upper tail.
Availability and version history
- Introduced: first introduction version is not established by the reviewed official history; the current product list is not a launch record.
- Availability: official help lists Excel for Microsoft 365, Excel for Microsoft 365 for Mac, Excel 2024, Excel 2024 for Mac, Excel 2021, Excel 2021 for Mac, Excel 2019, Excel 2016.
- Checked: October 14, 2026; official PROB reference. Documentation and independent models; no native Excel execution or wider platform certification.
Syntax and required evidence boundaries
Microsoft’s formal syntax marks both limits optional:
=PROB(x_range,prob_range,[lower_limit],[upper_limit])
The outcome range and associated probability range are required. The dedicated page does not explain the default event when the lower limit is omitted, so every worked formula here supplies it explicitly. The documented upper-limit omission rule is covered separately below.
The source requires equal data-point counts and probabilities summing to one. It assigns #N/A to unequal counts and #NUM! to an invalid probability total or probabilities outside its stated domain. Its prose specifically includes zero among rejected probabilities; zero-probability native behavior has not been tested here, so the examples use strictly positive weights and do not certify that boundary.
Example 1: an aligned probability table
Enter A1:B5:
| Outcome X | Probability |
|---|---|
| 0 | 0.1 |
| 1 | 0.2 |
| 2 | 0.3 |
| 3 | 0.4 |
The probabilities sum to 1. Each weight belongs to the outcome on the same row.
=PROB(A2:A5,B2:B5,1,2)
Expected result: 0.5, from probabilities 0.2 and 0.3. The boundaries are included, consistent with Microsoft’s worked interval example.
Formatting 0.5 as Percentage displays 50%. Do not enter probabilities 10,20,30,40 when the intended values are 10%,20%,30%,40%; those are different numeric inputs.
Example 2: omit only the upper limit
=PROB(A2:A5,B2:B5,2)
Expected result: 0.3, the probability that X equals 2. It is not the probability of X being at least 2.
For that upper-tail event in this finite table, supply the largest outcome explicitly:
=PROB(A2:A5,B2:B5,2,3)
Expected result: 0.7. The all-outcome interval from 0 through 3 has probability 1.
Advanced example: fractional limits can select whole outcomes
=PROB(A2:A5,B2:B5,0.5,2.5)
Expected result in the discrete-event model: 0.5. The only listed outcomes within those limits are 1 and 2. PROB does not spread each outcome’s probability smoothly over the gaps between listed values.
An interval from 10 to 20 includes no listed outcome, giving mathematical event probability 0. This is an independent empty-event calculation; mixed-type or reversed-limit native behavior is not inferred from it.
Advanced example: calculate a conditional event explicitly
Within the original distribution, the probability of X being at least 1 is 0.9, while the probability of X being at least 2 is 0.7.
=PROB(A2:A5,B2:B5,2,3)/PROB(A2:A5,B2:B5,1,3)
Expected result: 7/9, approximately 0.777778. This conditions on the event X≥1, whose probability is positive. The numerator event is contained within the denominator event.
The ratio is an additional probability calculation, not an undocumented conditional-mode argument to PROB. Check the event relationship and denominator before applying such a formula to another table.
Advanced example: normalize counts and distinguish expectation
Suppose observed category counts are 1,2,3,4 for outcomes 0,1,2,3. Their total is ten, and dividing each count by ten produces the example’s probability weights. Keep the original counts beside the normalized probabilities.
The expected outcome is 0*0.1+1*0.2+2*0.3+3*0.4=2. That expected value is not the point probability at X=2, which is 0.3. One is measured in outcome units; the other is a probability.
Validation and limits
Changing the final probability from 0.4 to 0.3 gives total 0.9 and reaches the documented invalid-total condition. Changing a weight without its associated outcome also changes the distribution. Sort outcome and probability columns together.
The reference’s exact-total requirement does not specify a universal floating-point tolerance. Duplicate outcomes, zero weights, omitted lower bounds, mixed types and reversed intervals remain outside the native evidence. Keep the small complete fixture available when diagnosing a larger report rather than hiding all invalid distributions behind a zero fallback.
References and verification
Expected outputs are independent mathematical calculations or explicitly documented rules, not captured native Excel results. Examples use fictional data, English function names and comma separators. Native floating-point boundaries remain untested.