The Hebrew word used here for "men" is "Ghever," and it is commonly associated with warfare. Exodus does not specify how or if the men were armed unless perhaps Exodus
Early probability Games of chance The modern mathematics of chance is usually dated to a correspondence between the French mathematicians Pierre de Fermat and Blaise Pascal in Suppose two players, A and B, are playing a three-point game, each having wagered 32 pistoles, and are interrupted after A has two points and B has one.
How much should each receive? Fermat and Pascal proposed somewhat different solutions, though they agreed about the numerical answer. Each undertook to define a set of equal or symmetrical cases, then to answer the problem by comparing the number for A with that for B. Fermat, however, gave his answer in terms of the chances, or probabilities.
He reasoned that two more games would suffice in any case to determine a victory. There are four possible outcomes, each equally likely in a fair game of chance. Of these four sequences, only the last would result in a victory for B.
Thus, the odds for A are 3: In that case, the positions of A and B would be equal, each having won two games, and each would be entitled to 32 pistoles.
A should receive his portion in any case. This first round can now be treated as a fair game for this stake of 32 pistoles, so that each player has an expectation of Games of chance such as this one provided model problems for the theory of chances during its early period, and indeed they remain staples of the textbooks.
Fermat and Pascal were not the first to give mathematical solutions to problems such as these.
More than a century earlier, the Italian mathematician, physician, and gambler Girolamo Cardano calculated odds for games of luck by counting up equally probable cases. His little book, however, was not published untilby which time the elements of the theory of chances were already well known to mathematicians in Europe.
It will never be known what would have happened had Cardano published in the s. It cannot be assumed that probability theory would have taken off in the 16th century. Cardano, moreover, had no great faith in his own calculations of gambling odds, since he believed also in luck, particularly in his own.
In the Renaissance world of monstrosities, marvels, and similitudes, chance—allied to fate—was not readily naturalized, and sober calculation had its limits. It was, for example, used by the Dutch mathematician Christiaan Huygens in his short treatise on games of chance, published in Every shuffle of a deck of cards leads to a card sequence that has low a priori probability, but has unit probability once the cards are all on the table.
Similarly, the "fine-tuning" of the constants of physics, said to be so unlikely, could very well have been random; we just happen to be in the universe that turned up in that particular deal of the cards.
The Table of Contents lists the main sections of the Mathematics Subject initiativeblog.com each heading may be found some links to electronic journals, preprints, Web sites and pages, databases and other pertinent material.
Your friends and colleagues are talking about something called "Bayes' Theorem" or "Bayes' Rule", or something called Bayesian reasoning.
They sound really enthusiastic about it, too, so you google and find a webpage about Bayes' Theorem and. The Table of Contents lists the main sections of the Mathematics Subject initiativeblog.com each heading may be found some links to electronic journals, preprints, Web sites and pages, databases and other pertinent material.
Essay on Statistical Methods and Probability - According to Chesemore (), statistics is concerned with methods based on mathematics theory and probability, which allows the user to summarize many observations concisely. The "traditional" view is that Eastern European Jews descend almost entirely from French and German Jews.
This essay presents the pros and cons of the controversial "Khazar theory" of Eastern European Jewish origins and will attempt to provide a likely middle-ground solution to the question.