How Should I Interpret P(A and B|C)?

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The expression P(A and B|C) should be interpreted as P((A and B)|C), indicating the probability of both A and B occurring given C. The alternative interpretation P(A and (B|C)) is considered nonsensical because P(B|C) represents a conditional probability, not an event that can be intersected. Participants in the discussion agree on the first interpretation and acknowledge the confusion surrounding the second. Overall, clarity in interpreting conditional probabilities is essential for accurate understanding. The consensus reinforces the importance of proper notation in probability theory.
alexei_kom
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Hello everybody!

Should I interpret the expression P(A and B|C) as P((A and B)|C) or as P(A and (B|C))?

Or the last expression has no meaning because P(B|C) is a ratio and I can't make an intersection with a ratio?



Thanks,

Alexei.
 
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I interpet it as the first. And you're right, the second expression doesn't make much sense...
 
micromass said:
I interpet it as the first. And you're right, the second expression doesn't make much sense...

Thank you very much!
 
I was reading documentation about the soundness and completeness of logic formal systems. Consider the following $$\vdash_S \phi$$ where ##S## is the proof-system making part the formal system and ##\phi## is a wff (well formed formula) of the formal language. Note the blank on left of the turnstile symbol ##\vdash_S##, as far as I can tell it actually represents the empty set. So what does it mean ? I guess it actually means ##\phi## is a theorem of the formal system, i.e. there is a...

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