BINO Function (Calligra Sheets)

• Introduced: First release not established; the name is present in Calligra 2.4.0 source.
• Supported in: Calligra Sheets 26.08.2, with no retirement established.
• Scope: Desktop Sheets with the Statistical module. Examples use English semicolon-separated formulas.
• Checked: October 14, 2026. Selected formulas ran through the official 25.04.2 engine library. Source and independent mathematics were checked. This is engine evidence, with no GUI-cell or import verification; 26.08.2 was source-checked only.

BINO calculates the probability of exactly m successes in n independent trials with a constant success probability p. Its argument order is trials, successes, probability. For valid integer counts, the mathematical expression is C(n,m)p^m(1−p)^(n−m). It is a point probability, not a cumulative probability or inverse distribution. Function help.

=BINO(trials;successes;probability)

Exactly three arguments are registered. Use nonnegative integer trials, integer successes with 0≤successes≤trials, and 0≤probability≤1. The source explicitly validates p but does not enforce the integer count domain. The combination helper converts counts to integers while the powers still use the original arguments, so fractional inputs do not define a coherent alternative binomial model. Registration and implementation.

The engine and mathematical columns are separate. Results are rounded to twelve decimal places, or thirteen significant digits in scientific notation for very small or large values. This is a display choice, not an accuracy guarantee. NaN and infinity are nonfinite outputs; an engine error flag is checked separately from those values.

For ten fair trials, the chance of exactly three successes is C(10,3)/2^10=120/1024=0.1171875. =BINO(10;3;0.5) returns that value. The probability of zero successes is 1/1024, not zero.

Use this model only when the number of trials is fixed, trials are independent and each trial has the same success probability. A varying success rate or sampling without replacement needs a different probability model. Label the inputs so the trials-first order is not accidentally swapped with another product’s successes-first syntax.

For one trial, the probabilities of zero and one success add to 1. The displayed advanced composition confirms that identity for p=0.3. This is a small exact normalization check; it does not validate every invalid count accepted by the wrapper.

The retained invalid examples are deliberately not probabilities: BINO(5;6;0.5) returns approximately −0.005208333333, and BINO(−1;1;0.5) returns 2. The low-count factorial helper returns −1 for negative factorial arguments, and the outer formula continues its arithmetic instead of rejecting the count.

The executed advanced check was:

=BINO(1;0;0.3)+BINO(1;1;0.3)

Its engine result was 1.

Fractions are especially misleading. BINO(5;2.9;0.5) happens to return 0.3125, while BINO(5.9;2;0.5) returns about 0.167464603521 because its exponent still contains 5.9. Neither is a valid integer-trial binomial request. The registered INVBINO compatibility name also has a separate arity mismatch; it is not recommended as an interchangeable working formula. This guide documents BINO only.

• Function-specific implementation
• Versioned function help
• Combin helper

The statistical module and value-calculation helpers are byte-identical between the inspected 25.04.2 and 26.08.2 sources. That comparison supports the source discussion but does not establish later-version native output, every locale or arbitrary extreme-parameter accuracy.

COMBIN.