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Here goes the problem:

Suppose there is a disease that infects one in ten thousand people. Suppose a test procedure determines whether you have the disease with 99% accuracy--that is, if you have the disease there is a 1% chance of a false negative, and if you don't have the disease there is a 1% chance of a false positive. You took the test and the test result is positive. What is the probability that you have the disease?

The solution to the problem is---0.98%.

Now, here lies my confusion, if the test can detect my disease with 99% accuracy then shouldn't I have a 99% chance of having the disease? Probably, I am asking the dumbest question ever asked but I just can't work my intuition through this.

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No.

The accuracy of a diagnosis prodecure is irrelevant to how likely is it that you have the disease.

Consider the most extreme case where you have the perfect diagnosis that has $100\%$ accuracy. It doesn't make you to have the disease.

However, if the test accuracy is high and it diagnoses that you have the disease, then the probability that you have the disease is high.

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  • $\begingroup$ I was mixing up probability and statistics. They are not always the same, I realize now. Just because 100 people were diagnosed right does not mean that 101st person will be done so. Thanx!! $\endgroup$ – abu obaida Nov 2 '19 at 10:41

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