Notations: probability

[Function]

Hello everyone

 

In class, we saw some stuff in probability and I wondered if they could also be written with these symbols:

 

[math]P(A \; \text{and}\; B)=P(A\cap B)[/math]

[math]P(A \; \text{or}\; B)=P(A\cup B)[/math]

 

And so I also wondered if they could also be written with proposition logic symbols

 

[math]P(A\wedge B)[/math] and [math]P(A\vee B)[/math]

 

For the chance of 'not A', we saw this notation: [math]P(\bar{A})[/math], but I wonder if this: [math]P(\neg A)[/math] is also good, and which one is the 'best' (best known, most correct one).

 

Thanks.

 

F

Edited March 31, 2014 by Function

[John]

What we have is a set of potential outcomes of an experiment (the "sample space"), which we'll denote with Ω, and individual outcomes are subsets of the sample space. In addition, we have a function P : Ω → [0,1] assigning a probability to each outcome. So when we say P(A ∪ B), we're talking about a union of subsets being assigned a probability. The propositional logic symbols don't entirely make sense in this context.

 

I suppose you could have a situation where you're randomly generating strings of logical symbols along with the two statements A and B, in which case the string "A ∧ B" would be one potential output. But of course, that's not the meaning you're asking about.

 

Edit: I should note, as always, that notation isn't sacred. You could use P(A ∧ B) to denote the probability of two events A and B both happening. But it'd be a little strange.

Edited March 31, 2014 by John

[Function]

Thanks