# Bayes theorem definition confusing

I'm reading through a lesson on Bayes theorem and I saw this slide:

How can model & data be == (data | model) x P(model)?

Does the & not imply multiplication? Otherwise it implies that data == data | model.

• Here $(A|B)$ means event A happens conditional on the event B happens. $(A \& B)$ means both event $A$ and $B$ happen. – user158565 May 25 '17 at 5:20

$P(Y = y \mid X = x) = \frac{P(X=x\ \,\cap\, Y=y)}{P(X=x)}$
The & sign is not multiplication, since in mathematics we do not use "&" to denote multiplication. It is what it is, it means probability of observing $X=x$ and $Y=y$ together. It leads to multiplication only when $X$ and $Y$ are independent.