Bay-Es-Ian

One of the blogs I read has an excellent discussion of Bayesian probabilities and one of their more prevalent applications, testing results. The example runs as such:

You have just tested positive for a disease that effects 1 in 10,000 people. The test is 99% accurate. At first pass, this sounds pretty bad and most are 99% confident that they would have the disease. However, you have hope! In a population of 1000 people, there would be 1% of people diagnosed with the disease, for which only 1 would actually have the disease and 99 would be false positives. So, for people diagnosed with the disease, there is actually only a 1% chance of having the disease, and 99% chance of being a false positive.

Now you're saying, this doesn't make any sense, there was only a 1% chance of the test being wrong, so how could I not have it if I was diagnosed? Yes, this is true, but that 1% chance of error is much larger than the 0.01% chance of having the disease.