Why are probabilities of false negative and false positive different? While it makes some sense, it's not clear to me why those are different. If a test, say medical test, is correct 90% of time then chances of it being wrong is 10%.
But I've read things that say in medical field test with high accuracy for negatives are used as screening method and more expensive tests which are high accuracy positive tests are used only when former tests come positive. Because if former came negative we are confident patient doesn't have a disease but if it comes positive we are not as sure, thus we do expensive test. Which of course, makes sense.
I get there are 4 events:


*

*Test is +, patient has a disease

*Test is -, patient doesn't have a disease

*Test is +, patient doesn't have a disease

*Test is -, patient has a disease

 A: To understand why the rate of false positives and false negatives should be different, you can consider the two edge cases: the constant tests. 
One “test” I could perform is by declaring every result a positive, regardless of any information about the input. I just say that it’s a positive result no matter what. Clearly, in this case, we’re going to get a lot of false positives (unless the result really should be positive for everything in the population), but we’re not going to get any false negatives because we never report anything to be negative.
Likewise, I could perform the “test” where I declare every single result to be negative, and hence I may get a bunch of false negatives but it is impossible for me to get any false positives since I never report anything as positive.
In both of these tests it’s really obvious why the rate of false positives doesn’t match the rate of false negatives. 
In general any other test you perform can be thought of as some kind of piecewise combination of these two tests, so it’s actually really quite rare that you’d be able to construct a test with the same likelihood of false positives and false negatives.
