A particular disease affects 0.1% of the population.   The test is 95% accurate.   You test positive.   What is the chance that you have the disease?  How I approached the problem: Since I already tested positive, and the question clearly states that the test is 95% accurate, there should be a 95% probability that I have the disease. But, a YouTube  says that the chance I have the disease is 2%. How is my reasoning wrong?
We are conducting a test on a rare disease. A positive result means that, according to the test, the subject is infected. The following characteristics are known about the test and the disease: If a person is infected, the person has a $95\%$ chance of testing positive. When a healthy person is tested, the test has a $99\%$ chance of giving a negative result. A mere $0.1\%$ of the population is infected with the disease. If a person is tested positive for the disease. What is the probability that the person actually has the disease? I don't understand how to write the conditional probabilities if someone can explain to me than I should know how to solve it, but I'm not sure how to convert the text into the mathematics language.
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