Is Bayes' Theorem ever applicable where tree diagrams aren't?

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I am currently revising for my end of year exam in maths, and have been going over probability and Bayes' Theorem. I really dislike having to learn formulae to use in exams and saw that the way Bayes' Theorem was derived was fundamentally from tree diagrams.

Does this mean that given an exam question in which I'd be expected to use Bayes' Theorem, I could really just draw a tree diagram? (This is theoretical as I understand it may need too many branches to be practical.)

If this is not true, what situations are there in which I would be unable to use tree diagrams and would have to retreat to blindly using equations?

Thanks very much for any help!