I show how probabilities arise in quantum physics by exploring implications of {it environment - assisted invariance} or {it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly entangled ``Bell-like states can be used to rigorously justify complete ignorance of the observer about the outcome of any measurement on either of the members of the entangled pair. For more general states, envariance leads to Borns rule, $p_k propto |psi_k|^2$ for the outcomes associated with Schmidt states. Probabilities derived in this manner are an objective reflection of the underlying state of the system -- they represent experimentally verifiable symmetries, and not just a subjective ``state of knowledge of the observer. Envariance - based approach is compared with and found superior to pre-quantum definitions of probability including the {it standard definition} based on the `principle of indifference due to Laplace, and the {it relative frequency approach} advocated by von Mises. Implications of envariance for the interpretation of quantum theory go beyond the derivation of Borns rule: Envariance is enough to establish dynamical independence of preferred branches of the evolving state vector of the composite system, and, thus, to arrive at the {it environment - induced superselection (einselection) of pointer states}, that was usually derived by an appeal to decoherence. Envariant origin of Borns rule for probabilities sheds a new light on the relation between ignorance (and hence, information) and the nature of quantum states.
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