Really basic quantum mechanics question

barnflakes
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I keep reading about qubits, and they say that if a qubit is represented as \arrowvert \phi \rangle = \alpha|0\rangle + \beta|1\rangle then the probability of it being in the 0 state is |\alpha^2| and similarly for the 1 state.

My question is how do they get this value? Is it from |\langle 0 | \phi \rangle|^2 ?
 
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Thread 'Is a table levitating possible, even at a minuscule probability?'

I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
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