 Understanding standards of proof in terms of mathematical probabilities is controversial. It is said to raise a number of paradoxes (Cohen 1977; Allen 1986, 1991; Allen and Leiter 2001; Redmayne 2008). Let us return to our previous example. The defendant, Blue Bus Company, owns 75% of the buses in the town where the plaintiff was injured by a recklessly driven bus and the remaining 25% is owned by Red Bus Company. No other evidence is presented. Leaving aside the reference class problem discussed above, there is a 0.75 probability that the accident was caused by a bus owned by the defendant. On the probabilistic interpretation of the applicable standard of proof (that is, the balance of probabilities), the evidence should be sufficient to justify a verdict in the plaintiff’s favour. But most lawyers would agree that the evidence is insufficient. Another familiar hypothetical scenario is set in the criminal context (Nesson 1979: 1192–1193). Twenty five prisoners are exercising in a prison yard. Twenty four of them suddenly set upon a guard and kill him. The remaining prisoner refuses to participate. We cannot in the ensuing confusion identify the prisoner who refrained from the attack. Subsequently, one prisoner is selected randomly and prosecuted for the murder of the guard. Those are the only facts presented at the trial. The applicable standard is proof beyond a reasonable doubt. Assume that the probabilistic threshold of this standard is 0.95. On the statistical evidence, there is a probability of 0.96 that the defendant is criminally  liable.[18]  Despite the statistical probability of liability exceeding the threshold, it is widely agreed that the defendant must be acquitted. In both of the examples just described, why is the evidence insufficient and what does this say about legal standards of proof?