Well, to calculate P(T|S) = p you need a model of how a student ‘works’, in such a way that the test’s result T happens for the kind of students S with probability p. Or you can calculate P(S|T), thereby having a model of how a test ‘works’ by producing the kind of student S with probability p. If you have only one of those, these are the only things you can calculate.
If on the other hand you have one or more complementary models (complemenetary here means that they exclude each other and form a complete set), then you can calculate the probabilities P(T1|S1), P(T1|S2), P(T2|S1) and P(T2|S2). With these numbers, via Bayes, you have both P(T|S) and P(S|T), so it’s up to you to decide if you’re analyzing stundents or tests. Usually one is more natural than the other, but it’s up to you, since they’re models anyway.
Well, to calculate P(T|S) = p you need a model of how a student ‘works’, in such a way that the test’s result T happens for the kind of students S with probability p. Or you can calculate P(S|T), thereby having a model of how a test ‘works’ by producing the kind of student S with probability p.
If you have only one of those, these are the only things you can calculate.
If on the other hand you have one or more complementary models (complemenetary here means that they exclude each other and form a complete set), then you can calculate the probabilities P(T1|S1), P(T1|S2), P(T2|S1) and P(T2|S2). With these numbers, via Bayes, you have both P(T|S) and P(S|T), so it’s up to you to decide if you’re analyzing stundents or tests.
Usually one is more natural than the other, but it’s up to you, since they’re models anyway.