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Bob wants to guess the maximal number with the highest possible probability, while Alice's goal is to keep this probability as low as possible. The difference with the basic secretary problem are two: Alice does not have to write numbers uniformly at random. She may write them according to any joint probability distribution to trick Bob.
A collection of puzzles involving numbers, logic, and probability 1962 Nov: Some puzzles based on checkerboards: 1962 Dec: Some simple tricks and manipulations from the ancient lore of string play: 1963 Jan: The author pays his annual visit to Dr. Matrix, the numerologist: 1963 Feb: Curves of constant width, one of which makes it possible to ...
As for the equal probability of the permutations, it suffices to observe that the modified algorithm involves (n−1)! distinct possible sequences of random numbers produced, each of which clearly produces a different permutation, and each of which occurs—assuming the random number source is unbiased—with equal probability.
The USMLE Step 1 consists of 280 multiple-choice questions administered over an eight-hour period. The exam covers topics such as anatomy, biochemistry, pharmacology, and physiology, among others. Scores used to be reported on a three-digit scale, but as of February 2022 is reported as pass/fail.
The Newton–Pepys problem is a probability problem concerning the probability of throwing sixes from a certain number of dice. [1] In 1693 Samuel Pepys and Isaac Newton corresponded over a problem posed to Pepys by a school teacher named John Smith. [2] The problem was: Which of the following three propositions has the greatest chance of success?
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[50] [13] [49] The conditional probability of winning by switching is 1/3 / 1/3 + 1/6 , which is 2 / 3 . [2] The conditional probability table below shows how 300 cases, in all of which the player initially chooses door 1, would be split up, on average, according to the location of the car and the choice of door to open by the host.
LONDON (Reuters) -Bitcoin broke $100,000 on Thursday as investors bet on a friendly U.S. regulatory shift, while world stocks touched fresh record highs with sentiment bolstered by upbeat comments ...
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