Statistics: Why doesn't the probability of an accurate medical test equal the probability of you having disease? Suppose there is a test for Disease A that is correct 90% of the time. You had this test done, and it came out positive. I understand that the chance that this test is right is 90%, but I thought this would mean the chance that you have a disease should be 90% too. However, according to Bayes' rule, your chance of disease depends on the percentage of the population that has this disease. It sounds absurd: If the test is correct then you have it, and if it's not then you don't, 90% of the time- so there should be 90% chance that the results are right for you...
But on other hand, say 100% of population has it. Then regardless of the chance the test says you have it, let it be 90% or 30%, your chance is still 100%... now all of a sudden it doesn't sound absurd.
Please avoid using weird symbols as I'm not statistics expert. It just deludes things for me and buries the insight.

Let's say 1/1000 people have a disease and we test 1000 people with a 10% fail rate on a test.

In this instance (1000 people) I haven't shown any false negatives. If we were showing 10,000 people we could include one.
