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After choosing a box at random and withdrawing one coin at random that happens to be a gold coin, the question is what is the probability that the other coin is gold. As in the Monty Hall problem, the intuitive answer is 1 / 2 , but the probability is actually 2 / 3 .
While a monkey is used as a mechanism for the thought experiment, it would be unlikely to ever write Hamlet, according to researchers.. The infinite monkey theorem states that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time will almost surely type any given text, including the complete works of William Shakespeare.
A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. They pick one envelope at random but before they open it they are given the chance to take the other envelope instead. [1]
Each of the n i occurrences of the i-th letter matches each of the remaining n i − 1 occurrences of the same letter. There are a total of N(N − 1) letter pairs in the entire text, and 1/c is the probability of a match for each pair, assuming a uniform random distribution of the characters (the "null model"; see below). Thus, this formula ...
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.
Here's the difference between choosing your own lotto numbers versus using a random number generator. ... You can choose the exact numbers you want or you can take advantage of Quick Pick and get ...
Choose A Letter: Guests pick a letter, and then must spell a given animal name without using that letter. Feelings: Guests must identify an item by touch and then spell it. Flags: Guests pick words from a board covered in flags, national or otherwise. Hard Words For a 13 Year Old: Guests are each joined by a 13-year-old, who may win a prize.
Occupancy problem: the distribution of the number of occupied urns after the random assignment of k balls into n urns, related to the coupon collector's problem and birthday problem. Pólya urn: each time a ball of a particular colour is drawn, it is replaced along with an additional ball of the same colour.