I'm not sure if this qualifies as a mathematical question but I'm really confused.
Take F to be the event “the fingerprints of the suspect match those at the crime scene” and I to be "the suspect is innocent".
A prosecution lawyer argues that there is a 1 in 50,000 chance of the suspect being innocent
Why is 1/50,000 tied to P(F|I) and not P(I|F)?
Is there a way to always get it right? I'm afraid when I'm doing the exam, I'll write the conditional the wrong way round. Any tips?
The way you have stated it, it is neither of those. You have clearly said "there is a 1 in 50,000 chance of the suspect being innocent", which means $$P(I)=\tfrac{1}{50000}\ .$$ For general advice, you could translate the conditional sign as "given" (often stated this way) or "supposing we know that" (less formal but possibly useful). So you could ask "supposing we know that the fingerprints match, what is the probability that the suspect is innocent?". The answer would be $P(I\mid F)$. Or maybe what you want to ask is "supposing we know that the suspect is innocent, what is the probability that the fingerprints match?". Then it would be $P(F\mid I)$. "What is the probability that the fingerprints match, given that the suspect is innocent?" is also $P(F\mid I)$: slightly tricky as the word order makes it look at bit like the previous example. You need to sort out clearly what is the event whose probability you want, and what is the condition or restriction or assumption which tells you what particular situation you are considering.
Not sure if this is part of what is causing you difficulties, but it may be worth pointing out that $A\mid B$ is not a set, and $P(A\mid B)$ is not the probability of a set in the same sense as $P(A\cap B)$ is the probability of a set. The former is just the probability of $A$, but under certain conditions.
Word problems are always tricky and in the end the only way to improve is to practise. However I hope these ideas help.