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I have come across both $P(\dots)$ and $\Pr(\dots)$ being used to represent probabilities. Is there any difference in the meaning of these notations, or are they just different shorthands?

I seem to come by $\Pr(\dots)$ more often in Bayesian probability contexts, though I wouldn't say that's a rule.

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  • $\begingroup$ I use both indifferently, but if you have a whole bunch of them in an expression, using $P$ instead of $\Pr$ may make the difference between whether or not the expression fits on a single line. $\endgroup$ – MPW Jul 22 '14 at 23:36
  • $\begingroup$ As you might know, the average of a certain variable $x$ can be expressed as $\langle x \rangle$ or $\bar{x}$ and probably there are other ways as well. No notation is fundamentally preferred, people learn a certain way, stick to it and eventually if they publish a book you get to read the notation they like. $\endgroup$ – Squirtle Jul 22 '14 at 23:48
  • $\begingroup$ I personally use $\mathbb P$ (blackboard bold). $\endgroup$ – Math1000 Feb 3 '20 at 19:08
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They are just different conventions.   They don't signify any different meaning.

I personally find the $\Pr$ notation most useful when the discussion involves combinatorics.   It distinguishes probability somewhat from permutation. (Unless you use ${^n{\rm P}_r}$ ...)

It also has that convenient LaTeX command \Pr which renders it in times roman font, and with some space padding, which helps it stand out in a line of multiplied probabilities using just a few keystrokes.

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They are just different notation. Some authors even use the blackboard bold font: $\mathbb{P}$. What matters is what's inside of the subsequent parentheses (or sometimes brackets, [].)

Several notation species exist for expectation ($E, \text{E},\mathbb{E}$) and variance ($V, \text{V},Var, \mathbb{V}$) too, but they all have the same definition.

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In classical approach to probability defined by Laplace, probability is the ratio of number of favourable cases to the total number of equally likely cases. Here probability of occurrence of A is denoted by P(A). Symbolically, if an event A can happen in 'a' ways out to total 'n' ways then the probability of occurrence of the event is denoted by Pr(A)=a/n

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