I dwell on the appearance, in the mid-19th century, of a formula describing random sampling without replacement under incomplete knowledge and discuss the statistical aspect of this formula and its applications. I also provide illustrations showing that the fairness of sampling without replacement was being questioned.

The use of such concepts as randomness and probability is discussed and stochastic decisions occurring in the sacred texts are studied. In connection with probability, the measurements made in antiquity in order to comply with religious demands are also touched on. The cases where cause rather than randomness was recognized to be at work are indicated, and the statements contained in the Talmud and the thoughts of its later commentator, Maimonides, on hypotheses are linked with the appropriate opinions of Isaac (...) Newton and Jakob Bernoulli. (shrink)