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2. Boy or girl paradox - Wikipedia

   en.wikipedia.org/wiki/Boy_or_Girl_paradox

   Specifically, that two different procedures for determining that "at least one is a boy" could lead to the exact same wording of the problem. But they lead to different correct answers: From all families with two children, at least one of whom is a boy, a family is chosen at random. This would yield the answer of ⁠ 1 / 3 ⁠. From all ...

3. Monte Carlo method - Wikipedia

   en.wikipedia.org/wiki/Monte_Carlo_method

   Monte Carlo simulation: Drawing a large number of pseudo-random uniform variables from the interval [0,1] at one time, or once at many different times, and assigning values less than or equal to 0.50 as heads and greater than 0.50 as tails, is a Monte Carlo simulation of the behavior of repeatedly tossing a coin.

4. Derangement - Wikipedia

   en.wikipedia.org/wiki/Derangement

   Derangement. Permutation of the elements of a set in which no element appears in its original position. Number of possible permutations and derangements of a collection elements that number n. n! (n factorial) is the number of n -permutations; !n (n subfactorial) is the number of derangements – n -permutations where all of the n elements ...

5. Kirkman's schoolgirl problem - Wikipedia

   en.wikipedia.org/wiki/Kirkman's_schoolgirl_problem

   In addition to S(2,3,9), Kramer and Mesner examined other systems that could be derived from S(5,6,12) and found that there could be up to 2 disjoint S(5,6,12) systems, up to 2 disjoint S(4,5,11) systems, and up to 5 disjoint S(3,4,10) systems. All such sets of 2 or 5 are respectively isomorphic to each other.

6. Bertrand's ballot theorem - Wikipedia

   en.wikipedia.org/wiki/Bertrand's_ballot_theorem

   The variant problem can be solved by the reflection method in a similar way to the original problem. The number of possible vote sequences is ( p + q q ) {\displaystyle {\tbinom {p+q}{q}}} . Call a sequence "bad" if the second candidate is ever ahead, and if the number of bad sequences can be enumerated then the number of "good" sequences can ...

7. Random permutation - Wikipedia

   en.wikipedia.org/wiki/Random_permutation

   A random permutation is a random ordering of a set of objects, that is, a permutation -valued random variable. The use of random permutations is common in games of chance and in randomized algorithms in coding theory, cryptography, and simulation. A good example of a random permutation is the fair shuffling of a standard deck of cards: this is ...

8. Combination - Wikipedia

   en.wikipedia.org/wiki/Combination

   Combination. In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter (unlike permutations). For example, given three fruits, say an apple, an orange and a pear, there are three combinations of two that can be drawn from this set: an apple and a pear; an apple ...

9. Fisher–Yates shuffle - Wikipedia

   en.wikipedia.org/wiki/Fisher–Yates_shuffle

   The problem here is that the low-order bits of a linear congruential PRNG with modulo 2 e are less random than the high-order ones: [6] the low n bits of the generator themselves have a period of at most 2 n. When the divisor is a power of two, taking the remainder essentially means throwing away the high-order bits, such that one ends up with ...