Function Posted March 31, 2014 Share Posted March 31, 2014 (edited) 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 Link to comment Share on other sites More sharing options...

John Posted March 31, 2014 Share Posted March 31, 2014 (edited) 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 1 Link to comment Share on other sites More sharing options...

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