PROB in Google Sheets: Discrete Events and Required Lower Limits

• Introduced: first introduction date is not established by the reviewed official history; no desktop release number is inferred.
• Availability: documented in the rolling Google Sheets service; these examples use the web worksheet workflow.
• Checked: October 14, 2026; official PROB reference. Documentation and independent models, with no native Sheets execution or wider client certification.

=PROB(data,probabilities,low_limit,[high_limit])

Google requires the data and probability arrays to contain the same number of values. Each probability must be greater than zero and no greater than one according to the dedicated reference. The optional high limit defaults to the low limit.

The complete body reviewed does not name exact error codes or specify a floating-point tolerance for a probability total. The examples use strictly positive weights summing exactly to one in rational arithmetic, making a complete distribution without extending those sparse native rules.

Keep each probability aligned with its outcome. Sorting just one column changes the distribution, even when all individual numbers remain present.

Enter A1:B5:

=PROB(A2:A5,B2:B5,2,5)

Expected result in the discrete-event model: 0.7, adding 0.3 and 0.4 for the two boundary-inclusive outcomes 2 and 5. The total probability of the complete table is one.

A Percentage format can display 0.7 as 70%. Entering the number 70 as a probability is not equivalent to entering 70% or 0.7.

=PROB(A2:A5,B2:B5,5)

Expected result: 0.4, the weight attached to outcome 5. Google’s default makes the event equality with the low limit.

To include both 5 and 9, explicitly supply the upper endpoint:

=PROB(A2:A5,B2:B5,5,9)

Expected result: 0.6. The all-outcome interval 0 through 9 has probability 1.

=PROB(A2:A5,B2:B5,3,8)

Expected result: 0.4. Only the listed outcome 5 lies in that interval. The function does not spread its 0.4 probability continuously over neighboring gaps in the outcome scale.

An interval from 3 through 4 contains no listed outcome and has mathematical event probability 0. This is an independent empty-event check; the exact native behavior of reversed limits or mixed text is not inferred from it.

The probability of X≥2 in the finite table is 0.9, while the probability of X≥5 is 0.6. The latter event is contained in the former.

=PROB(A2:A5,B2:B5,5,9)/PROB(A2:A5,B2:B5,2,9)

Expected conditional probability: 2/3, approximately 0.666667. The denominator is positive. This division is an additional probability calculation, not a hidden optional mode of PROB.

For a different table, first check the conditioning event and whether its probability is zero before performing an analogous division.

The expected outcome in this distribution is 0*0.1+2*0.3+5*0.4+9*0.2=4.4.

There is no outcome 4.4 in the table. The expected value summarizes a probability-weighted average in outcome units; it is not a probability. The most likely listed outcome is 5, whose probability is 0.4, illustrating a third distinct question.

Counts 1,3,4,2 total ten and normalize to the probability weights in the example. Keep the counts visible when those weights come from observed frequencies, rather than imply that a formula alone validates their statistical representativeness.

The reference’s strictly positive probability rule excludes zero from its documented input range; native zero-weight behavior remains untested. The page also leaves invalid-total handling, duplicate outcomes, nonnumeric inputs and exact error displays unspecified.

A mathematical probability distribution should have total weight one. If the final weight were changed from 0.2 to 0.1, the total would be 0.9 and the table would be incomplete as the stated distribution. This guide does not assign a Google error code to that untested case.

Retain the original outcomes and weights when diagnosing a report. A numeric result alone cannot show that the input probabilities describe the intended population or event.

• Google PROB reference.
• Editorial testing standards.

Examples use fictional data, English function names and comma separators. Expected outputs are independent mathematical calculations or explicitly documented rules, not native Sheets captures. Check the spreadsheet locale when reproducing punctuation-sensitive formulas.