first very happens next will be unrelated and we'll be able to simplify things okay so this is this is kind of really everything we need so we just need three things we need law of total probability the regular version and the conditioned version we need Bayes rule the regular version the conditioned version and we need a notion of conditional independence which will allow us to simplify equations this is also equivalent to writing and also we'll see it that way equivalent to px given Z and Y but once you know Z X is independent of Y being