题目

概率论一道题,求教
Do you have a rare disease?Suppose that 1 in 633 people have a particular disease.You go to the doctor and they suggest that you be tested for the disease.The test will accurately give a positive test result with probability 0.94,and will accurately give a negative test result with probability 0.81.If the test comes back positive,what is the probability you have the disease?

提问时间：2021-01-09

答案

A1表示患病,A2表示无病 ,B表示检查阳性
根据贝叶斯公式和全概公式,所求条件概率P(A1|B)=P(B|A1)P(A1)/[P(B|A1)P(A1)+P(B|A2)P(A2)]=(1/633 *0.94)/(1/633* 0.94 + 632/633 *0.19) =47/605 约为0.0078（由于无病误诊为阳性的概率0.19太高导致结果极不可信）