Math Problem Statement
假设你是一名医生。你以前的经验告诉你,一个酗酒者患肝病的概率是80%,而非酗酒者患肝病的概率是 10%。此外,你还知道总体上5%的病人是酗酒者 设事件“酗酒者”为A,“非酗酒者"为NA,患肝病为L,没有患肝病为NL。请用数学符号表达以下答案。 1.假设我们用贝叶斯定理来计算这个概率,请问这个人是酗酒者的概率的先验是什么? 2.一个人患肝病的非条件概率是多少? 3.给定你观察到某个人患有肝病,那这个人是酗酒者的概率是什么? 4如果你以前的经验有误差,实际上一个非酗酒者患肝病的概率是20%,那这个人 是酗酒者的后验概率是多少?
Solution
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Math Problem Analysis
Mathematical Concepts
Probability theory
Conditional probability
Bayesian theorem
Formulas
Bayes' theorem
Theorems
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Suitable Grade Level
Advanced undergraduate or graduate level
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