Say I wanted to find the probability of someone passing an exam. Then I could condition on this by how much preparation they had done for the exam. Let $E$ be the event of someone passing an exam and $F$ the event they had done sufficient preparation. So I write $$P(E) = P(E|F)P(F) + P(E|F^c)P(F^c)$$
However, I also think you can condition on whether someone passes by numerous other reasons: if they were ill, if their dog died, bereavement, financial difficulties, other commitments... So essentially, I could write the above eqn and get an infinite amount of terms.
Is this correct and if so, how would I know in some problem what event to condition on? If not correct, why? Many thanks