ABSTRACT

In the seventeenth and eighteenth centuries, two mathematicians were asked by gamblers to help them improve their chances of winning at cards and dice. The two mathematicians, who first studied this area of probability, were James Bernoulli and Abraham DeMoivre. James Bernoulli developed the formula for combinations and permutations, and their binomial expansions, which lead to the binomial distribution discussed in Chapter 17. Abraham DeMoivre coined the phrase law of errors from observing events such as archery matches. The basic idea was that negative errors occurred about as often as positive errors. DeMoivre used this understanding to derive an equation for an error curve. DeMoivre in 1733 was credited with developing the mathematical equation for the normal curve. In the nineteenth century, Carl Fredrick Gauss (1777-1855), working in the field of astronomy further developed the concept of a mathematical bell-shaped curve and probability. Today, his picture and mathematical equation for the normal curve appear on the zehn deutsche mark currency of Germany.