Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? This is a Bayes' Theorem problems.

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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11.) Upon arrival at a hospital emergency room, patients are categorized according to their conditions as critical, serious, or stable. In the past year:

(i) 10% were critical

(ii) 30% were serious

(iii) the rest were stable 

(iv) 40% of critical patients died

(v) 10% of serious patients died

(vi) 1% of stable patients died

Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? This is a Bayes' Theorem problems. 

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