Probability of having disease given positive test result I am trying to solve a puzzle and have struck in some fundamental concepts of probability.
In an epidemic, its found that only one in 10000 people actually suffer from the rare disease. So  the probability that I am positive will be

P1= 1/10000

But there is a medical test also which has 99% accuracy. Unfortunately my test result is positive. As per this test, the probability that I am positive will be

P2= 99/100

Now I have two probabilities P1 and P2.  The first question that comes to my mind is how can we have two probabilities for a single event (i.e. being "positive")? Why they are different?
Secondly, which one should I trust and why ?
Or what is the actual probability of me being found positive?
Edit
The specific question is if 100000 people are tested, and the test says I am positive, then what is the probability that I am actually suffering from the disease given the test results?

The question is not so basic as it may seem.
It concerns the notion of pre-test and post-test probability. Assuming that both these probabilities P1 and P2 were given to you by the test lab, and are not implied by somebody else, here's how they relate to each other.
P1 is a prevalence metric, it tells you how likely it is that a random person has a disease without knowing anything about the person.
P2 is the probability that you have the disease given that you tested positive. Again, here I'm assuming that you got P2 from the lab explicitly. This is important because you may have found the accuracy 99% somewhere and simply assumed that it's the probability. This would have been wrong as explained further.
This example has relevant equations. Here's how it works. A test has a sensitivity and specificity, i.e. how well it can classify positive and negative cases. These two metrics give you positive test likelihood ratio as $$R=\frac{sensitivity}{1-specificity}$$
Using P1 you obtain pretest odds, before knowing anything about your lab result the odds of having a disease are:$$\pi=\frac{P1}{1-P1}$$
Now you can calculate the post test odds, i.e. odds of having disease after lab results came back positive:$$\pi_p=\pi R$$
Finally we convert post-test odds into probability:$$P2=\frac{\pi_p}{1+\pi_p}$$
You can see how the pre-test probability P1 enters into post-test probability P2. However, it is not possible to work the numbers out because we need to know sensitivity and specificity of the test for that. Knowing only the accuracy of the test is not enough for that. You can lookup the definition of accuracy metric and see that yourself. Reported Accuracy of the tool also depends on prevalence of disease in the test population.
Notice how dramatically changes the probability of having disease post test, i.e. after receiving the lab result. It is because the test has a good discriminating ability.
