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What is the probability of winning the car by switching given the player has picked door 1 and the host has opened door 3? The answer to the first question is 2 / 3 , as is shown correctly by the "simple" solutions. But the answer to the second question is now different: the conditional probability the car is behind door 1 or door 2 ...
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?
Graphs of probabilities of getting the best candidate (red circles) from n applications, and k/n (blue crosses) where k is the sample size. The secretary problem demonstrates a scenario involving optimal stopping theory [1] [2] that is studied extensively in the fields of applied probability, statistics, and decision theory.
Probability distribution of the length of the longest cycle of a random permutation of the numbers 1 to 100. The green area corresponds to the survival probability of the prisoners. In the initial problem, the 100 prisoners are successful if the longest cycle of the permutation has a length of at most 50.
Distribution of the 2898 answers to 1983 tie breaker Jeux et Stratégie contest. Alain Ledoux is the founding father of the "guess 2 / 3 of the average" game. In 1981, Ledoux used this game as a tie breaker in his French magazine Jeux et Stratégie. He asked about 4,000 readers, who reached the same number of points in previous puzzles ...
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 "68–95–99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal. It is also used as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal.
The National Board of Medical Examiners (NBME), founded in 1915, is a United States non-profit which develops and manages assessments of student physicians. Known for its role in developing the United States Medical Licensing Examination (USMLE) in partnership with the Federation of State Medical Boards (FSMB), USMLE examinations for medical students and residents are used by medical licensing ...
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