An English Presbyterian minister and a French mathematician forged a magic key which enables us to update our probabilistic judgements, use probability as a basis for reasoning without being a statistician, reconcile objective and subjective probability, combine observed frequency and calculated probability, and predict the probability of the next event.

The Bayes–Laplace rule

Thomas Bayes was the first person to use the concept of conditional probability, for which Pierre-Simon Laplace found a more widespread application. (See the box.) We presented this concept briefly in Chapter 4 on the escalating severity of nuclear accidents, more specifically in relation to the probability of massive release of radioactive material in the event of a core melt, or in other words given that core meltdown has occurred. This probability is denoted using a vertical bar: p(release|melt). In a general way, A and B being two events, the conditional probability is written as p(A|B), which reads as ‘the probability of A given B’. Or, to be more precise, we should refer to two conditional probabilities; as we are focusing on two events, we may also formulate the conditional probability p(B|A), the probability of B given A. In the case of a core melt and the release of radioactivity, p(melt|release) is almost equal to one: with just a few exceptions (water loss from a spent-fuel pool) a massive release is impossible unless the core has melted.