Say you get a positive result. This could be due to you being positive and the test working correctly (true positive), or you being negative and the test working incorrectly (false positive).
Say you get a negative result. This could be due to you being negative and the test working correctly (true negative), or you being positive and the test working incorrectly (false negative).
In terms of being one sample out of an entire population, you have a certain probability of being positive or negative (a priori probability). The test then also has a certain probability each of producing the four different scenarios outlined above (true / false positive, true / false negative).
So when you test people and get positive / negative numbers, what you get is the combination of these different probabilities, and you don't just know which bit is due to what.
How simply?
On the most basic level, it's like this:
Say you get a positive result. This could be due to you being positive and the test working correctly (true positive), or you being negative and the test working incorrectly (false positive).
Say you get a negative result. This could be due to you being negative and the test working correctly (true negative), or you being positive and the test working incorrectly (false negative).
In terms of being one sample out of an entire population, you have a certain probability of being positive or negative (a priori probability). The test then also has a certain probability each of producing the four different scenarios outlined above (true / false positive, true / false negative).
So when you test people and get positive / negative numbers, what you get is the combination of these different probabilities, and you don't just know which bit is due to what.