B in Zoho Sheet: Syntax and Worked Examples
Calculate exact or inclusive-range binomial probabilities with B; distinguish its argument order and interval contract from BINOMDIST.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer
B returns the probability of a specified count, or an inclusive range of counts, in a binomial model. For five independent trials with success probability 0.5, =B(5;0.5;2) has independent expected value 0.3125. Including both two and three successes with =B(5;0.5;2;3) gives 0.625.
The letter B is the function name here. It is not a reference to spreadsheet column B, and it is not an alternative spelling of BINOMDIST: their argument order and optional argument mean different things.
Syntax and model assumptions
=B(n; p; k; [k2])
n: number of independent trials.p: success probability for each trial.k: lower count of successes to include.k2: upper count to include; it defaults tok.
The official B reference describes these lower and upper bounds. The worked examples use nonnegative integer counts within 0…n, with k≤k2 and probabilities strictly between 0 and 1.
A binomial model assumes a fixed trial count, two outcomes per trial, independence and a common success probability. For example, five independent simulated trials with success probability 0.5 fit the mathematics. Real repeated observations are not automatically independent simply because they occupy different spreadsheet rows.
Step-by-step: exactly two successes
Enter A2=5, B2=0.5 and C2=2. Then use:
=B(A2;B2;C2)
The direct equivalent is =B(5;0.5;2). There are 5!/(2!Ă—3!) = 10 arrangements containing exactly two successes. Each specific arrangement has probability 0.5^2Ă—0.5^3 = 1/32. Therefore the independent expected result is 10/32 = 0.3125, or 31.25% when formatted as a percentage.
This is a probability, not an expected count of successes. The binomial expected count is nĂ—p = 2.5, which is a separate mathematical summary and need not be an integer. Nor is 31.25% a guarantee that exactly that fraction of a small collection of repeated experiments will show two successes.
Include an interval without double counting
Put D2=3 and enter =B(A2;B2;C2;D2). For the same five-trial model, all six possible counts have these exact probabilities:
| Successes | Number of arrangements | Probability |
|---|---|---|
| 0 | 1 | 1/32 |
| 1 | 5 | 5/32 |
| 2 | 10 | 10/32 |
| 3 | 10 | 10/32 |
| 4 | 5 | 5/32 |
| 5 | 1 | 1/32 |
The events “two successes” and “three successes” are mutually exclusive. Adding their probabilities gives 20/32 = 0.625. The endpoints are included, so the interval is not merely a cumulative probability through three successes.
Complete additional independent checks are:
| Formula | Event | Expected value |
|---|---|---|
=B(5;0.5;0;1) |
At most one success | 0.1875 |
=B(5;0.5;4;5) |
At least four successes | 0.1875 |
=B(5;0.5;2;5) |
At least two successes | 0.8125 |
=B(5;0.5;0;2) |
At most two successes | 0.5 |
=B(5;0.5;3;3) |
Exactly three successes | 0.3125 |
=B(5;0.5;0;5) |
All possible counts | 1 |
The full-range total supplies a useful arithmetic check. Do not sum overlapping ranges as though their events were disjoint.
Advanced example: unequal outcome probabilities
For four independent trials with success probability 0.25:
=B(4;0.25;1)
=B(4;0.25;1;2)
Exactly one success has probability 4Ă—0.25Ă—0.75^3 = 0.421875. Exactly two has probability 6Ă—0.25^2Ă—0.75^2 = 0.2109375. The inclusive interval therefore has independent expected probability 0.6328125. This example prevents a common shortcut: arrangements are equally likely within one fixed count, but the success and failure probabilities are not both 0.5.
Errors and compatibility
The brief help page does not specify exact numeric-error tokens or coercion rules for fractional counts, reversed bounds, invalid probabilities or counts exceeding n. The examples avoid those inputs; mathematical impossibility alone does not establish which error or value this implementation returns. Endpoint probabilities 0 and 1 are also not certified here.
BINOMDIST puts the success count before the trial count and offers a mode argument. B instead puts n first and uses its fourth argument as an upper count. Translating between them requires changing the formula’s meaning and arguments, not just its name. CRITBINOM addresses a probability-to-count threshold rather than the interval probability calculated here.
The rolling official reference was checked on October 18, 2026. Its first release and any retirement/deprecation history are not established. These examples were independently calculated and were not executed in the Zoho application or engine; imported-workbook and mobile behavior are untested.