What probability riddle originally published in American Statistician in 1975 gained popular attention after it was featured in Parade in 1990?
"Monty Hall problem The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based 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 , . It became famous as a question from a reader's letter quoted in Marilyn vos Savant's ""Ask Marilyn"" column in ""Parade"" magazine in 1990 : Vos Savant's response was that the contestant should switch to the other door . Under the standard"
"including those below. (All puzzles published from October 23, 1996, on are available to online subscribers to the ""Times"" crossword.) A few crosswords have achieved recognition beyond the community of crossword solvers. Perhaps the most famous is the November 5, 1996 puzzle by Jeremiah Farrell, published on the day of the U.S. presidential election, which has been featured in the movie ""Wordplay"" and the book ""The Crossword Obsession"" by Coral Amende, as well as discussed by Peter Jennings on ABC News, featured on CNN, and elsewhere. The two leading candidates that year were Bill Clinton and Bob Dole; in Farrell's"
"Newspaper riddle The newspaper riddle is a riddle joke or conundrum that begins with the question: The traditional answer, which relies upon the identical pronunciation of the words ""red"" and ""read"", is: Barrick believes this riddle to be ""perhaps the most common example of a folk riddle collected in the United States in the twentieth century"", pointing out that between 1917 and 1939 it appeared in 15 collections of folk riddles, and in a further six between 1939 and 1974. Alternative answers to the riddle exist, where red is used as a color, parodying the canonical form of the riddle."
"gave the correct answer that switching would win two-thirds of the time, she estimates the magazine received 10,000 letters including close to 1,000 signed by PhDs, many on letterheads of mathematics and science departments, declaring that her solution was wrong. Due to the overwhelming response, ""Parade"" published an unprecedented four columns on the problem. As a result of the publicity the problem earned the alternative name Marilyn and the Goats. In November 1990, an equally contentious discussion of vos Savant's article took place in Cecil Adams's column ""The Straight Dope"" (Adams 1990). Adams initially answered, incorrectly, that the chances for"
"letter presented the problem in a version close to its presentation in ""Parade"" 15 years later. The second appears to be the first use of the term ""Monty Hall problem"". The problem is actually an extrapolation from the game show. Monty Hall ""did"" open a wrong door to build excitement, but offered a known lesser prize – such as $100 cash – rather than a choice to switch doors. As Monty Hall wrote to Selvin: A version of the problem very similar to the one that appeared three years later in ""Parade"" was published in 1987 in the Puzzles section"
"statistics can generate. Martin Gardner wrote a popular account of Simpson's paradox in his March 1976 Mathematical Games column in ""Scientific American"". Edward H. Simpson first described this phenomenon in a technical paper in 1951, but the statisticians Karl Pearson et al., in 1899, and Udny Yule, in 1903, had mentioned similar effects earlier. The name ""Simpson's paradox"" was introduced by Colin R. Blyth in 1972. One of the best-known examples of Simpson's paradox is a study of gender bias among graduate school admissions to University of California, Berkeley. The admission figures for the fall of 1973 showed that men"
"this variant, the player can have different probabilities of winning depending on the observed choice of the host, but in any case the probability of winning by switching is at least (and can be as high as 1), while the overall probability of winning by switching is still exactly . The variants are sometimes presented in succession in textbooks and articles intended to teach the basics of probability theory and game theory. A considerable number of other generalizations have also been studied. The version of the Monty Hall problem published in ""Parade"" in 1990 did not specifically state that the"
"into account that the warden may have tossed a coin before he gave his answer. The warden may have answered formula_2 because formula_1 is to be released and he tossed a coin. Or, formula_3 is to be released. But the probabilities of the two events are not equal. Judea Pearl (1988) used a variant of this example to demonstrate that belief updates must depend not merely on the facts observed but also on the experiment (i.e., query) that led to those facts. Three Prisoners problem The Three Prisoners problem appeared in Martin Gardner's ""Mathematical Games"" column in ""Scientific American"" in"
"newspaper column by Marilyn vos Savant in 1990. A host (""Monty"") provides a player with three doors, one containing a valuable prize and the other two containing a ""gag"", valueless prize. The contestant is offered a choice of one of the doors without knowledge of the content behind them. ""Monty"", who knows which door has the prize, opens a door that the player did not select that has a gag prize, and then offers the player the option to switch from their choice to the other remaining door. The probability problem arises from asking if the player should switch to"
"was required remained open until 1990, when it was convincingly solved as ""seven shuffles,"" as elaborated below. Some results preceded this, and refinements have continued since. A leading figure in the mathematics of shuffling is mathematician and magician Persi Diaconis, who began studying the question around 1970, and has authored many papers in the 1980s, 1990s, and 2000s on the subject with numerous co-authors. Most famous is , co-authored with mathematician Dave Bayer, which analyzed the Gilbert–Shannon–Reeds model of random riffle shuffling and concluded that the deck did not start to become random until five good riffle shuffles, and was"
"which a horse is running to the left and the other to the right, one upside up, and the other upside down. Famous Trick Donkeys Famous Trick Donkeys is a puzzle invented by Sam Loyd in 1858, first printed on a card supposed to promote P.T. Barnum's circus. At that time, the puzzle was first called ""P.T. Barnum's trick mules"". Millions of cards were sold, with an estimated income for Sam Loyd of $10,000 from 1871—about $200,000 in 2014 dollars. In 1858 Sam Loyd thought of a puzzle card that consisted on two mules and two riders. Dividing the card"
"Boy or Girl paradox The Boy or Girl paradox surrounds a set of questions in probability theory which are also known as ""The Two Child Problem"", ""Mr. Smith's Children"" and the ""Mrs. Smith Problem."" The initial formulation of the question dates back to at least 1959, when Martin Gardner published one of the earliest variants of the paradox in ""Scientific American"". Titled ""The Two Children Problem"", he phrased the paradox as follows: Gardner initially gave the answers and , respectively, but later acknowledged that the second question was ambiguous. Its answer could be , depending on how you found out"
"Merriam-Webster, publishers of the leading American dictionaries, first heard of this puzzle in a letter dated March 17, 1975, from Patricia Lasker of Brooklyn, New York. Lasker says her plant manager heard the question on an unnamed quiz show. Since that time Merriam-Webster has received about four letters each year asking the question. The puzzle first appears in print in Anita Richterman's ""Problem Line"" column in ""Newsday"" on April 29, 1975. One ""M.Z."" from Wantagh, New York states that the problem was asked on a TV quiz program. Richterman states that she asked a learned professor of English for help"
"today, having endured in the popular imagination for over 50 years. In 1992, the ""Skeptical Inquirer"" ran a ""Spooky Presidential Coincidences Contest."" One winner found a series of sixteen similar coincidences between Kennedy and former Mexican President Álvaro Obregón, while the other came up with similar lists for twenty-one pairs of US Presidents. An example of the list is presented here for illustration. Some urban folklorists have postulated that the list provided a way for people to make sense of two tragic events in American history by seeking out patterns. Gardner and others have said that it is relatively easy"
"most common assumption, as the purpose of the riddle was most likely to trick the listener into making long winded calculations only to be surprised by the simplicity of the answer. If one disregards the 'trick' answer and assumes the narrator overtook the group as they were ""also"" travelling to St. Ives, the most common mathematical answer is 2802: 1 man, 7 wives, 49 sacks, 343 cats, and 2401 kits, plus the narrator (the sum of a geometric series, plus one). After the riddle was published in the August 4, 1779 issue of ""The Weekly Magazine"", as described above, a"
"is what is the probability that the other coin is gold. As in the Monty Hall problem, the intuitive answer is , but the probability is actually . The Three Prisoners problem, published in Martin Gardner's ""Mathematical Games"" column in ""Scientific American"" in 1959 (1959a, 1959b), is equivalent to the Monty Hall problem. This problem involves three condemned prisoners, a random one of whom has been secretly chosen to be pardoned. One of the prisoners begs the warden to tell him the name of one of the others to be executed, arguing that this reveals no information about his own"
"1962 until their deaths; Marilyn predeceased her husband by four months. Hall died from heart failure on September 30, 2017, at his home in Beverly Hills at the age of 96. He was interred at Hillside Memorial Park Cemetery on October 3. Hall's name is used in a probability puzzle known as the ""Monty Hall problem"". The name was conceived by statistician Steve Selvin who used the title in describing a probability problem to ""Scientific American"" in 1975 based on one of the games on ""Let's Make a Deal"", and more popularized when it was presented in a weekly national"
"Bertrand paradox (probability) The Bertrand paradox is a problem within the classical interpretation of probability theory. Joseph Bertrand introduced it in his work ""Calcul des probabilités"" (1889) as an example to show that probabilities may not be well defined if the ""mechanism"" or ""method"" that produces the random variable is not clearly defined. The Bertrand paradox goes as follows: Consider an equilateral triangle inscribed in a circle. Suppose a chord of the circle is chosen at random. What is the probability that the chord is longer than a side of the triangle? Bertrand gave three arguments, all apparently valid, yet"
"that one child was a boy. The ambiguity, depending on the exact wording and possible assumptions, was confirmed by Bar-Hillel and Falk, and Nickerson. Other variants of this question, with varying degrees of ambiguity, have been popularized by Ask Marilyn in ""Parade Magazine"", John Tierney of ""The New York Times"", and Leonard Mlodinow in ""Drunkard's Walk"". One scientific study showed that when identical information was conveyed, but with different partially ambiguous wordings that emphasized different points, that the percentage of MBA students who answered changed from 85% to 39%. The paradox has frequently stimulated a great deal of controversy. Many"
"Bertrand's box paradox Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in his 1889 work ""Calcul des probabilités"". There are three boxes: The 'paradox' is in the probability, after choosing a box at random and withdrawing one coin at random, if that happens to be a gold coin, of the next coin drawn from the same box also being a gold coin. These simple but counterintuitive puzzles are used as a standard example in teaching probability theory. Their solution illustrates some basic principles, including the Kolmogorov axioms. It may seem that the probability"
"Zebra Puzzle The zebra puzzle is a well-known logic puzzle. Many versions of the puzzle exist, including a version published in ""Life International"" magazine on December 17, 1962. The March 25, 1963, issue of ""Life"" contained the solution and the names of several hundred solvers from around the world. The puzzle is often called Einstein's Puzzle or Einstein's Riddle because it is said to have been invented by Albert Einstein as a boy; it is also sometimes attributed to Lewis Carroll. However, there is no known evidence for Einstein's or Carroll's authorship and the ""Life International"" version of the puzzle"
"Petals Around the Rose Petals Around the Rose is a mathematical challenging puzzle in which the object is to work out the formula by which a number is derived from the roll of a set of five or six dice. It is often used as an exercise in inductive reasoning. The puzzle became popular in computer circles in the mid 1970s, particularly through an anecdote recounted in ""Personal Computing"" which depicts Bill Gates working out the solution in an airport. The puzzle is commonly presented as a game in which one person rolls the dice and announces a numerical result"
"famous during the 1840 United States presidential election, is based on the third, fourth and seventh chapters from ""The House at Pooh Corner"" by A. A. Milne. During the fall, Tigger has been bouncing on anyone he comes across for fun, especially Rabbit when he is gardening, which makes Rabbit angry, so he decides to arrange a meeting with Pooh and Piglet and formulate a plan to prevent Tigger from bouncing: abandon Tigger in the woods, and find him the next day so hopefully Tigger will stop bouncing on his friends unexpectedly. Initially the plan seems to work, but when"
"it raises several issues at the foundations of knowledge representation and uncertain reasoning: the relationships between fallibility, corrigible belief and logical consequence; the roles that consistency, statistical evidence and probability play in belief fixation; the precise normative force that logical and probabilistic consistency have on rational belief. Although the first published statement of the lottery paradox appears in Kyburg's 1961 ""Probability and the Logic of Rational Belief"", the first formulation of the paradox appears in his ""Probability and Randomness"", a paper delivered at the 1959 meeting of the Association for Symbolic Logic, and the 1960 International Congress for the History"
"such as the Monty Hall Problem and the Bertrand's box paradox) is because of the use of naive heuristics that fail to properly define the number of possible outcomes. Boy or Girl paradox The Boy or Girl paradox surrounds a set of questions in probability theory which are also known as ""The Two Child Problem"", ""Mr. Smith's Children"" and the ""Mrs. Smith Problem."" The initial formulation of the question dates back to at least 1959, when Martin Gardner published one of the earliest variants of the paradox in ""Scientific American"". Titled ""The Two Children Problem"", he phrased the paradox as"
"Lindley's paradox Lindley's paradox is a counterintuitive situation in statistics in which the Bayesian and frequentist approaches to a hypothesis testing problem give different results for certain choices of the prior distribution. The problem of the disagreement between the two approaches was discussed in Harold Jeffreys' 1939 textbook; it became known as Lindley's paradox after Dennis Lindley called the disagreement a paradox in a 1957 paper. Although referred to as a ""paradox"", the differing results from the Bayesian and frequentist approaches can be explained as using them to answer fundamentally different questions, rather than actual disagreement between the two methods."
"of ""The Journal of Economic Perspectives"" (Nalebuff 1987). Nalebuff, as later writers in mathematical economics, sees the problem as a simple and amusing exercise in game theory. Phillip Martin's article in a 1989 issue of ""Bridge Today"" magazine titled ""The Monty Hall Trap"" (Martin 1989) presented Selvin's problem as an example of what Martin calls the probability trap of treating non-random information as if it were random, and relates this to concepts in the game of bridge. A restated version of Selvin's problem appeared in Marilyn vos Savant's ""Ask Marilyn"" question-and-answer column of ""Parade"" in September 1990. Though vos Savant"
"Jeremiah Farrell Jeremiah (Jerry) Farrell (born 1937) is an American professor emeritus of mathematics at Butler University in Indiana. He is well known for having designed Will Shortz's favorite puzzle, the 1996 ""Election Day"" crossword in ""The New York Times"". He has also written puzzles for many other books and newspapers, such as Scott Kim's puzzle column for ""Discover"" magazine. Farrell was born in Hastings, Nebraska, the oldest of three children to Belle Einsphar, and Paul Farrell, a third generation railroad man. Farrell himself worked for one summer on the railroad, as a ""grinder"", whose job was to plane down"
"the poem to Poe - and solved the riddles. See the page on eapoe.org for more. A riddle poem in a modified sonnet form, ""An Enigma"" was published in March 1848 in the ""Union Magazine of Literature and Art"" under its original simple title ""Sonnet."" Its new title was attached by Rufus Wilmot Griswold. Its lines conceal an anagram with the name Sarah Anna Lewis (also known as ""Stella""). Lewis was an amateur poet who met Poe shortly after the death of his wife Virginia while he lived in Fordham, New York. Lewis's husband paid Poe $100 to write a"
"""amazing"" feat, and said it's his favorite puzzle. With his wife Karen, Farrell has helped to organize the biannual Gathering for Gardner conferences, which started in 1993 as an invitation-only event for people connected with Martin Gardner. In 2006 Farrell and his wife took over from A. Ross Eckler, Jr. as editors and publishers of the quarterly publication """", established in 1968. Jeremiah Farrell Jeremiah (Jerry) Farrell (born 1937) is an American professor emeritus of mathematics at Butler University in Indiana. He is well known for having designed Will Shortz's favorite puzzle, the 1996 ""Election Day"" crossword in ""The New"
"(controlled by, but more lax than, the Oxford English Dictionary) added ""hangry"" on 27 August 2015, and the full Oxford English Dictionary added ""hangry"" in 2018. There are anecdotal reports of various forms of the puzzle dating to the 1950s or earlier; the ultimate origin is presumably an oral tradition or a lost book of puzzles. However, the first documented evidence is from early 1975 in the New York metropolitan area, and the puzzle rapidly gained popularity in this year. The most likely source is the talk show of Bob Grant, from some program in early or mid March 1975."
"or you can have the other two doors, one of which (a non-prize door) I'll open for you."" Adams did say the ""Parade"" version left critical constraints unstated, and without those constraints, the chances of winning by switching were not necessarily two out of three (e.g., it was not reasonable to assume the host always opens a door). Numerous readers, however, wrote in to claim that Adams had been ""right the first time"" and that the correct chances were one in two. The ""Parade"" column and its response received considerable attention in the press, including a front-page story in the"
"for ties. Puzzle contests started to gain widespread popularity in the 1920s, and in 1927 the tabloid newspaper the ""New York Evening Graphic"" offered $50,000 in a contest. By the 1940s and 1950s millions of players tried to solve puzzles published in a wide range of newspapers and magazines. The first puzzle contests in that era were designed primaily to boost the circulation of the magazine or newspaper. These contests were usually free to play. The most popular contest of this era was the Tangle Towns contest. Shortly after the ""New York Herald Tribune"" started publishing Tangle Towns in September"