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Problems of the following type, and their solution techniques, were first studied in the 18th century, and the general topic became known as geometric probability. ( Buffon's needle ) What is the chance that a needle dropped randomly onto a floor marked with equally spaced parallel lines will cross one of the lines?
Bertrand expressed the solution as. where is the total number of voters and is the number of voters for the first candidate. He states that the result follows from the formula. where is the number of favourable sequences, but "it seems probable that such a simple result could be shown in a more direct way".
An Essay Towards Solving a Problem in the Doctrine of Chances is a work on the mathematical theory of probability by Thomas Bayes, published in 1763, [1] two years after its author's death, and containing multiple amendments and additions due to his friend Richard Price. The title comes from the contemporary use of the phrase "doctrine of ...
One problem was the so-called problem of points, a classic problem already then (treated by Luca Pacioli as early as 1494, [5] and even earlier in an anonymous manuscript in 1400 [5]), dealing with the question how to split the money at stake in a fair way when the game at hand is interrupted half-way through. The other problem was one about a ...
Balls into bins problem. The balls into bins (or balanced allocations) problem is a classic problem in probability theory that has many applications in computer science. The problem involves m balls and n boxes (or "bins"). Each time, a single ball is placed into one of the bins. After all balls are in the bins, we look at the number of balls ...
Coupon collector's problem. In probability theory, the coupon collector's problem refers to mathematical analysis of "collect all coupons and win" contests. It asks the following question: if each box of a given product (e.g., breakfast cereals) contains a coupon, and there are n different types of coupons, what is the probability that more ...
Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.Two events are independent, statistically independent, or stochastically independent [1] if, informally speaking, the occurrence of one does not affect the probability of occurrence of the other or, equivalently, does not affect the odds.
The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work Calcul des probabilités (1889) [1] as an example to show that the principle of indifference may not produce definite, well-defined results for probabilities if it is applied uncritically when the domain of possibilities is infinite.