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Multiple choice questions lend themselves to the development of objective assessment items, but without author training, questions can be subjective in nature. Because this style of test does not require a teacher to interpret answers, test-takers are graded purely on their selections, creating a lower likelihood of teacher bias in the results. [8]
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?
The Rademacher distribution, which takes value 1 with probability 1/2 and value −1 with probability 1/2. The binomial distribution, which describes the number of successes in a series of independent Yes/No experiments all with the same probability of success.
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 than t boxes need to be bought ...
Formally, a multivariate random variable is a column vector = (, …,) (or its transpose, which is a row vector) whose components are random variables on the probability space (,,), where is the sample space, is the sigma-algebra (the collection of all events), and is the probability measure (a function returning each event's probability).
Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in various fields of science, engineering, and mathematics, such as physics, chemistry, biology, statistics ...
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.
Then considering the case with p = a and q = b, the last vote counted is either for the first candidate with probability a/(a + b), or for the second with probability b/(a + b). So the probability of the first being ahead throughout the count to the penultimate vote counted (and also after the final vote) is: