Question about what field this problem would belong to

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The discussion focuses on calculating the probability of hospital claims that include operating room charges, given that 85% of claims have emergency room charges and 25% do not include emergency room charges. The independence of emergency room and operating room charges is a key factor in the probability calculation. Participants suggest studying basic probability concepts to solve the problem, with recommendations for free online resources and videos to aid understanding. The conversation emphasizes the need for foundational knowledge in probability theory to approach such questions effectively. Overall, mastering these concepts will facilitate solving similar problems in the future.
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An insurance company pays hospital claims. The number of claims that include emergency room or operating room charges is 85% of the total number of claims. The number of claims that do not include emergency room charges is 25% of the total number of claims. The occurrence of emergency room charges is independent of the occurrence of operating room charges on hospital claims.

Calculate the probability that a claim submitted to the insurance company includes operating room charges.


What would I need to study to solve this problem? Are there any resources that I can get for free online?
 
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This is a basic probability question. The videos here should help you with that.
 

Thread 'Deductive proof in logic formal systems'

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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