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As a mathematician, I often write and read about probabilities. In the literature, I've seen versions of all the sentences below. Which one is correct?

This happens with probability (of) 30%.

This happens with the probability (of) 30%.

This happens with a probability (of) 30%.

In particular, what article should one use and is "of" correct/necessary?

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    When I hear a weather report, it's of the form The chance of rain is 30%. When I read a math / statistics paper, I have seen With probability 0.30 and With a probability p=0.30 or With a p-value = 0.0235. I have rarely seen the definite article, e.g., With the probability of 0.30 simply because mathematicians rarely talk about 30% as the "one-and-only" 30%. .
    – rajah9
    Apr 20, 2021 at 10:56
  • English usage is at our question about articles. This appears to be jargon, though: a field-specific usage for mathematical academic literature.
    – Andrew Leach ♦
    Apr 20, 2021 at 10:59
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    Here's an NGram chart querying all relevant permutations. Showing that with a probability of 25% beats out article-less with probability 25% - the others (with a probability 25% with the probability 25%, with the probability of 25%) are all just too rare to chart.
    – FumbleFingers
    Apr 20, 2021 at 12:52
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    Agree with the comments above. Would add that when you give the shorter version ("The event occurs with probability 30%") you get a marginally more scientific/technical sound than when you use "a... of" (to my ears at least).
    – cruthers
    Apr 20, 2021 at 15:27

1 Answer 1

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I would say that:

This happens with probability 30%

Here adding 'of' would be ungrammatical. Whilst

This happens with a probability of 30%

Here the 'of' is necessary for the sentence to be gramatically correct.

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    Hello, Mozibur. While I agree that these sound the most natural (and my degrees are in science, and I taught maths/statistics), ELU expects answers to be backed by linked and attributed supporting references. // I'm not sure that this warrants the downvote, though. It would often be better if downvotes required reasons to be added.
    – Edwin Ashworth
    Apr 20, 2021 at 9:32

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