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I have been describing the probabilities that are greater than 0 as non-zero (using the fact that they cannot ever be negative) or positive, e.g., "non-zero probability" or "positive probability." I want to describe the probabilities less than 1 in a similar fashion. I got some ideas, but they didn't seem alright:

  • non-one; never heard this one in my life
  • non-unit; I've heard this one by itself but not in a phrase like "non-unit probability", and I suspect there might be something more appropriate when it comes to probabilities
  • non-complete (?)

Is there a single word to substitute the italicized phrase in the following:

"I can set this program to do its job with any non-unit probability of success you like."

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    $\begingroup$ Single word requests should be accompanied by the sentence in which the word will be used, $\endgroup$
    – Greybeard
    Commented Mar 11, 2023 at 11:36
  • $\begingroup$ This seems more like a question for the mathematics SE, since it's about terminology specific to that field. $\endgroup$
    – alphabet
    Commented Mar 11, 2023 at 13:22
  • $\begingroup$ The existing answer may well be correct, but I'm going to hand this over to domain experts. $\endgroup$ Commented Mar 11, 2023 at 16:50
  • $\begingroup$ Probability approaching one is "almost certain." Probability less than one is uncertain. You could use other qualifiers that might be more descriptive as to how uncertain. $\endgroup$
    – user317176
    Commented Mar 11, 2023 at 16:58

2 Answers 2

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One says that an event with probability one is a certain event, so I would suggest uncertain for an event with probability less that 1, but I am not a native english speaker, so I may be wrong.

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    $\begingroup$ But can't you have events that occur with probability one that are not certain? Take $X\sim\mathcal N(\mu,\sigma^2)$. The event $X\neq 1$ occurs with probability one but is not certain as it's still possible to observe $X=1$. $\endgroup$ Commented Mar 11, 2023 at 17:02
  • $\begingroup$ Maybe use almost certain for such events. $\endgroup$ Commented Mar 11, 2023 at 17:05
  • $\begingroup$ @AaronHendrickson It is a matter of definition. I have always learned that an event with probability 1 is a certain event, but some authors define a certain event as an event that necessarily occurs, which means that only $\Omega$ would be a certain event. $\endgroup$ Commented Mar 11, 2023 at 17:05
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I would suggest partial for this usage:

I can set this program to do its job with any partial probability of success you like.

This would stress that the probability is incomplete, i.e., not perfect or whole (not one).

partial adj
Of, relating to, being, or affecting only a part; not total; incomplete: The plan calls for partial deployment of missiles. The police have only a partial description of the suspect.
TFD Online

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  • $\begingroup$ I doubt that the reader will readily understand that the probability is less than 1 when they just see the phrase "partial probability" -- a simple parenthetical explanation for the first encounter can easily fix that. However, it would be better if the word was self-explanatory. "Non-unit" is self-explanatory, but doesn't sound very elegant. $\endgroup$ Commented Mar 11, 2023 at 21:32
  • $\begingroup$ The word leaves no room for ambiguity in English. A thing is either partial or it is complete. A partial probability is one that is not complete, and therefore, to extend it to mathematics, it is less than one. You asked this on EL&U, which is where I answered it. If you're looking for a precise mathematical term maybe you should go with "<1 probability" or something along those lines. $\endgroup$
    – Robusto
    Commented Mar 11, 2023 at 21:57
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    $\begingroup$ @Robusto To me, a "partial" probability would suggest one that hadn't been completely computed. $\endgroup$
    – user888379
    Commented Mar 12, 2023 at 0:42

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