Exactly! The mathematical aspect of Bayes' Theorem is a simple algebraic manipulation of conditional probabilities. Another way to intuitively justify your mid

Exactly! The mathematical aspect of Bayes' Theorem is a simple algebraic manipulation of conditional probabilities. Another way to intuitively justify your middle two equations is to visualise a Venn diagram with overlapping circles representing A and B, such that areas correspond to probabilities. Then P(B|A) is the area of the overlap - i.e. P(A,B) - divided by the area of A - i.e. P(A).