TITLE: Statistics: Why doesn't the probability of an accurate medical test equal the probability of you having disease?
QUESTION [24 upvotes]: 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.

REPLY [3 votes]: 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.

Let's change that 90% to 50%:
I have developed a software that analyzes your eye movements and detects if you have brain cancer. Because it's actually a difficult thing to do and I was lazy, I programmed the software just to flip a coin and tell YES or NO, with 50% chance each.
So, we have a test for Disease A that is correct 50% of the time. I had this test done, and it came out positive. Is the chance that the test was right 50%?