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The chapter discusses the development of probability theory and its application to decision-making in the eighteenth century. It begins with a story about a Soviet professor who, despite the statistical probability of being hit by a bomb during an air raid, only decided to take refuge in a shelter after an elephant was killed. This story illustrates the dual nature of probability, where past frequencies clash with personal beliefs when making risky decisions.

The chapter then introduces Jacob Bernoulli, who was the first to consider the relationship between probability and the quality of information. He recognized the limitations of probability theory, particularly its exclusive application to games of chance. Bernoulli proposed the idea of using sample data to calculate probabilities, but his approach was criticized by Leibniz. Despite this, Bernoulli persisted and published his work on probability in 1713. He defined probability as the degree of certainty and suggested that future events would follow a similar pattern to past events. However, he acknowledged the difficulty of finding real-life cases that met the requirement of independent observations.

Nicolaus Bernoulli, Jacob’s nephew, continued his work and published his own findings in 1718. He calculated the probability that a certain number of observations would fall within a specified range and introduced the concept of moral certainty. His work laid the foundation for statistical inference and marked a significant advancement in measuring uncertainty.

Abraham de Moivre, a mathematician living in England, further developed Jacob and Nicolaus Bernoulli’s work. He utilized the normal distribution and standard deviation to estimate the probability that a set of observations would fall within a specified bound. De Moivre’s work was widely recognized, and his curve became known as the bell curve.

The chapter also introduces Thomas Bayes, a minister and mathematician who published an influential essay in 1763, three years after his death. Bayes addressed the problem of determining the true average ratio of defectives based on a sample of observations. His essay laid the foundation for modern statistical inference and provided a method for calculating the probability of an unknown given certain data.

The chapter concludes with the recognition of Richard Price, a mathematician and minister who received Bayes’s papers after his death. Price made significant contributions to the development of mortality tables for life insurance and annuities. Despite some errors in his calculations, his work established actuarial science and made him the founding father of the field.

Overall, the chapter discusses the advancements in probability theory and their applications in decision-making during the eighteenth century. It highlights the importance of quality information and the challenges of measuring uncertainty in real-life situations. The work of Jacob and Nicolaus Bernoulli, as well as de Moivre and Bayes, laid the foundation for modern statistical inference and had a significant impact on the field of probability theory.

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