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  2. Balls into bins problem - Wikipedia

    en.wikipedia.org/wiki/Balls_into_bins_problem

    (All the bounds hold with probability at least / for any constant >.) Note that for m > n log ⁡ n {\displaystyle m>n\log n} , the random allocation process gives only the maximum load of m n + O ( log ⁡ log ⁡ n ) {\displaystyle {\frac {m}{n}}+O\left(\log \log n\right)} with high probability, so the improvement between these two processes ...

  3. Stars and bars (combinatorics) - Wikipedia

    en.wikipedia.org/wiki/Stars_and_bars_(combinatorics)

    The solution to this particular problem is given by the binomial coefficient (+), which is the number of subsets of size k − 1 that can be formed from a set of size n + k − 1. If, for example, there are two balls and three bins, then the number of ways of placing the balls is ( 2 + 3 − 1 3 − 1 ) = ( 4 2 ) = 6 {\displaystyle {\tbinom {2 ...

  4. Sunrise problem - Wikipedia

    en.wikipedia.org/wiki/Sunrise_problem

    A reference class problem arises: the plausibility inferred will depend on whether we take the past experience of one person, of humanity, or of the earth. A consequence is that each referent would hold different plausibility of the statement. In Bayesianism, any probability is a conditional probability given what one knows. That varies from ...

  5. Coupon collector's problem - Wikipedia

    en.wikipedia.org/wiki/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 than t boxes need to be bought ...

  6. Problem of points - Wikipedia

    en.wikipedia.org/wiki/Problem_of_points

    The problem of points, also called the problem of division of the stakes, is a classical problem in probability theory.One of the famous problems that motivated the beginnings of modern probability theory in the 17th century, it led Blaise Pascal to the first explicit reasoning about what today is known as an expected value.

  7. Newton–Pepys problem - Wikipedia

    en.wikipedia.org/wiki/Newton–Pepys_problem

    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?

  8. List of probability distributions - Wikipedia

    en.wikipedia.org/wiki/List_of_probability...

    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.

  9. Urn problem - Wikipedia

    en.wikipedia.org/wiki/Urn_problem

    In probability and statistics, an urn problem is an idealized mental exercise in which some objects of real interest (such as atoms, people, cars, etc.) are represented as colored balls in an urn or other container. One pretends to remove one or more balls from the urn; the goal is to determine the probability of drawing one color or another ...