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I'm learning about the conditional probabilities and need some help in solving a example: Suppose a test method gives positive results for the infected person 65% of time and negative results for healthy person 99.93% of the time. In the language of false negative & false positive-> false negative rate is 35%, while false positive rate is 0.07%. Now the question is if someone tested positive what is the probability that they are infected? The percent of total population infected is 0.05%

From comment: I'm getting 31.7% chances are there of someone tested positive has the disease. I just want to cross check my result.

Henry
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Advaita
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    What have you tried? If you had a hundred million people, how many people would you expect to be infected and how many of those would you expect to test positive? How many people would you expect to not be infected and how many of those would you expect to test positive? – Henry Apr 26 '22 at 10:11
  • Yes! I'm getting 31.7% chances are there of someone tested positive has the disease. I just want to cross check my result. If total number of people are 100 million then 0.05% of them are infected and 99.95% are healthy. The answer of your last question is there in terms of false positive and false negative. – Advaita Apr 26 '22 at 10:23
  • $31.7%$ looks like a reasonable rounded answer for $\frac{0.0005 \times 0.65} { 0.0005 \times 0.65 + 0.9995\times 0.0007}$ – Henry Apr 26 '22 at 10:26
  • Thanks for confirming!! – Advaita Apr 26 '22 at 10:28
  • @Advaita Here's my answer to a similar question. – ryang Apr 26 '22 at 11:16

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