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:
1. Test is +, patient has a disease
2. Test is -, patient doesn't have a disease
3. Test is +, patient doesn't have a disease
4. Test is -, patient has a disease