Published on July 2, 2025 7:27 PM GMT

I've got some insight on the Bayes' theorem. 

P(A|B) = P(B|A) P(A) / P(B).

Can't we switch the thing into:

P(A|B) =  P(A)[P(B|A) / P(B)] .

In that way,  P(A|B) equals to the P(A) times ratio of P(B|A) / P(B). It means P(A|B) is just the ratio of P(B|A) / P(B) in P(A). It's much more simpler this way.

And from that, we can also change it to:

P(A|B)/P(A) =  P(B|A) / P(B) .

Which means the two ratio should be correct. It means this theorem assumes that these 2 ratio should be the same.

I wondered why so many textbooks, YouTube, wiki never explains it this way. It's much simpler this way.