Quantum mechanics is non-commutative probability

Quantum mechanics is traditionally meant to be difficult to understand. I think this is just a scam perpetrated by the physicists, because actually it’s all very simple. 

We’ll review the basics of probability theory, and reveal the secret that with an apparently minor tweak to the axioms (allowing non-commutative algebras, such as two-by-two matrices, as well as commutative ones, such as complex-valued functions on a set) we obtain a unified view of both classical and quantum mechanics. I’ll explain how Bayes’ law — which explains how to update one’s probabilistic knowledge of the world, based on a new observation — has a natural generalisation explaining measurement in quantum mechanics. Time permitting I’ll describe Bell’s theorem, demonstrating that there are genuinely new probabilistic phenomena arising in quantum mechanics.