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Case 1

The probability that event A equals to 1, B equals to 2, and C equals to 3 is X.

and

The probability that event A equals to 1; B equals to 2, and C equals to 3 is X.

which is correct?

My concern here is according to "https://data.grammarbook.com/blog/commas/how-to-punctuate-between-sentences-using-commas-semicolons-and-colons/", it states that

"Rule: Use the semicolon if you have two independent clauses connected without a conjunction"

I am not sure if this rule applies to 3 clauses, and if it does apply,

The probability that event A equals to 1; B equals to 2, and C equals to 3 is X.

looks very weird to me.

Case 2

The probability that (1) event A equals to 1, (2) B equals to 2, and (3) C equals to 3 is X.

and

The probability that (1) event A equals to 1; (2) B equals to 2, and (3) C equals to 3 is X.

which is correct?

There is a need to use (1), (2), (3) because my original sentence for "event A equals to 1" is actually quite long. In case2, which way to use "semicolon" is correct?

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Yu-Cheng Chen!

We usually use commas in lists within a sentence:

I believe that dogs are fun, cats are lazy, and pets are a lot of work.

Semicolons are used between to highly connected thoughts, almost like a conjunction:

He ran all night and was utterly exhausted by the ordeal; he collapsed.

So, the better formulation given your example is the first:

The probability that event A equals to 1, B equals to 2, and C equals to 3 is X.

That's because our brains conceptualize this as:

The probability that event 'A equals to 1', 'B equals to 2', and 'C equals to 3' is X.
The probability that event 'A=1', 'B=2', and 'C=3' is X.

As a math guy, I'd probably write:

The probability that event A=1, B=2, and C=3 is P.

Note well, in very sophisticated writing, sometimes semicolons are used, but rarely in common usage.

Be such that the claims in the book need to be addressed, which is the purpose of this exegesis, then one can conclude certain ideas are tenable such as: the nature of man must be explored soley by philosophers who by their method are more apt to the characteristics of man clearly, no insult meant to other professions; that to explore any collection of human traits is a process which requires time, energy, and a peculiar attention to the psychological is beyond doubt; and it is no small victory for a personality framework to include such a comprehensive and sweeping set of ontological and epistemological features, and thus I give credit where credit is due.

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Semicolons go between two parts of a sentence when each is technically a sentence. "He was victorious in yesterday's mayoral race; work begins now."

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