Help me understand this example of applying Bayes' Theorem

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This discussion focuses on the application of Bayes' Theorem in the context of conditional probability. The user seeks clarification on the equivalence of two expressions involving the joint probability P(X,Y,Z) and its relation to Bayes' Theorem. The key takeaway is that both expressions represent the same conditional probability framework, demonstrating how Bayes' Theorem can be applied to derive one from the other. Understanding this equivalence is crucial for mastering probabilistic reasoning.

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I'm reviewing some notes regarding probability, and the section regarding Conditional Probability gives the following example:

HB3ZTal.gif


The middle expression is clearly just the application of Bayes' Theorem, but I can't see how the third expression is equal to the second. Can someone please clarify how the two are equal?
 

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The numerator is P(X,Y,Z) in both cases.
 
Thank you!
 

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