There are about 7000 people with AIDS in HK (prevalence = 0.1)
If there is a good screening test that
1) everyone carrying AIDS will test +ve.
2) 99% of those without AIDS will test -ve
Suppose you have tested positive, what is the chance of you actually carrying the disease? ( Steps Plz )
Simple Prob.
2011-01-21 7:24 pm
回答 (2)
2011-01-21 9:20 pm
✔ 最佳答案
Let N : normal people, D : Diseased people. P(N) = 99.9%; P(D) = 0.1%
P(positive | D) = 1; P(positive | N) = 1 - 99% = 0.01
P(positive)
= P(positive | D)P(D) + P(positive | N)P(N)
= (1)(0.001) + (0.01)(0.999)
= 0.01099
P(D | positive)
= P(positive | D)P(D)/P(positive)
= 0.001 /0.01099
= 0.09099181
~9%
So, if the test of a man is positive, the chance of he actually carrying the disease is near to 9%.
2011-01-21 7:34 pm
Population of HK = 7000000
Prevalence of AIDS in HK = 0.1% = 10^3 (Necessary amendment... too scary if the prevalence is 10%...)
Judging from your content, I assume that all 7 million people in HK are taking the screening test.
Number of people tested to be +ve = 7000000[10^3+(1-10^3)(1-0.99)]
= 7000000(0.01099)
= 76930
Probability of you actually carrying the disease = 7000/76930
= 0.09099181
= 9.099181%
Prevalence of AIDS in HK = 0.1% = 10^3 (Necessary amendment... too scary if the prevalence is 10%...)
Judging from your content, I assume that all 7 million people in HK are taking the screening test.
Number of people tested to be +ve = 7000000[10^3+(1-10^3)(1-0.99)]
= 7000000(0.01099)
= 76930
Probability of you actually carrying the disease = 7000/76930
= 0.09099181
= 9.099181%
收錄日期: 2021-04-26 14:05:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110121000051KK00282