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The Monty Hall problem is a brain teaser, in the form of a probability puzzle, based nominally on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975.
Monty Hall problem, also known as the Monty Hall paradox: [2] An unintuitive consequence of conditional probability. Necktie paradox: A wager between two people seems to favour them both. Very similar in essence to the Two-envelope paradox. Proebsting's paradox: The Kelly criterion is an often optimal strategy for maximizing profit in the long ...
Like the Monty Hall problem, the "two boys" or "second-sibling" problem predates Ask Marilyn, but generated controversy in the column, [24] first appearing there in 1991–1992 in the context of baby beagles: A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're male, female, or a pair.
In 2009, Adam S. Landsberg proposed the following simpler variant of the 100 prisoners problem which is based on the well-known Monty Hall problem: [13] Behind three closed doors a car, the car keys and a goat are randomly distributed. There are two players: the first player has to find the car, the second player the keys to the car.
Two envelopes problem; Sleeping Beauty problem; The Monty Hall and Three Prisoners problems are identical mathematically to Bertrand's Box paradox. The construction of the Boy or Girl paradox is similar, essentially adding a fourth box with a gold coin and a silver coin. Its answer is controversial, based on how one assumes the "drawer" was chosen.
The three prisoners problem appeared in Martin Gardner's "Mathematical Games" column in Scientific American in 1959. [ 1 ] [ 2 ] It is mathematically equivalent to the Monty Hall problem with car and goat replaced respectively with freedom and execution.
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The article cites Gillman (1992) in support of the Morgan et al. solution. Interestingly Gillman does not refer to those authors at all, but instead to a note by himself one year earlier "The car and goats fiasco", Focus (newsletter of the Mathematical Association of America, of which Gillman was a past president), volume (or number) 11, June 2011, p.8.