How can I interprete ROC-curves? (example inside) I will be writing an exam in machine learning and am preparing for it.
During my studies I encountered ROC-curves but I can't wrap my head around what they actually tell you.
I have the following ROC-curves: 

First of all the x-Axis is false-alarms, the y-Axis is the hits.
Now the questions from old exams was to say which of these curves would be better for 


*

*image recognition for smartphones

*testing somebody for the ebola-virus/bomb-detector at an airport


Intuitively, the first one should have many hits, the second one can have false alarms, since I want to be sure that if there is a bomb, I recognize it. If there is no bomb I still tolerate false alarms, since better be safe than sorry, right?
But which of the both curves A and B belong to which statement? What do the curves mean?
 A: Traditionally, with screening tests for a disease one seeks an ROC curve
that bends up near the upper-left corner, such as "A." Also, a curve that dips
below the 45-degree line (separating upper-left from lower right)
is not favored. 
False alarms for diseases and bomb threats
are expensive (extra expensive 'gold standard' testing required,
inconvenience discourages participation). However, ebola is hardly a typical disease.
If there are too many false alarms at an airport
the method falls out of use because of the excessive disruption.
"Better safe than sorry" is hard to argue against until you
face the consequences of it.
Depending on user's personality and needs, "B" might be OK for an
iPhone. Maybe lots of false alarms are tolerated because of the
advantage of correct IDs which may be reminders ("Oh yeah, Sven Rasmusson, the prospective Swedish client from the happy hour last month.") , vs. false
alarms that could be instantly dismissed as "Somebody I never
heard of."
IMHO you are being asked a mainly-philosophical question rather than
a mathematical one, which may not be totally appropriate for such
an exam. Might be OK if there is a suitable philosophical discussion
in the course that gives clues to the author's opinion. For an exam
question, the author's opinion is the only thing that matters.
Anyhow, it seems your main question was how to understand the curve. Maybe
this answer will help with that. Maybe other Answers will be more
helpful with the philosophical issues--towards a 'correct' answer
to the exam question.
