  Do chances exist? The best examples of probability functions that meet the principles about chance are those provided by our best physical theories. In particular, the probability functions that feature in radioactive decay and quantum mechanics have some claim to being chance functions. In orthodox approaches to quantum mechanics, some measurements of a system in a given state will not yield a result that represents a definite feature of that prior state (Albert 1992). So, for example, an \(x\)-spin measurement on a system in a determinate \(y\)-spin state will not yield a determinate result reflecting some prior state of \(x\)-spin, but rather has a 0.5 probability of resulting in \(x\)-spin \(= +1\), and a 0.5 probability of resulting in \(x\)-spin \(= -1\). That these measurement results cannot reflect any prior condition of the system is a consequence of various no-hidden variables theorems, the most famous of which is Bell’s theorem (Bell 1964; see the entry on Bell’s  theorem,  Shimony 2009).  Bell’s theorem shows that the probabilities predicted by quantum mechanics, and experimentally confirmed, for spin measurements on a two-particle entangled but spatially separated system cannot be equal to the joint probabilities of two independent one-particle systems. The upshot is that the entangled system cannot be represented as the product of two independent localised systems with determinate prior \(x\)-spin states. Therefore, there can be no orthodox local account of these probabilities of measurement outcomes as reflecting our ignorance of a hidden quality found in half of the systems, so that the probabilities are in fact basic features of the quantum mechanical systems  themselves.[4]