Statistical Paradoxes - Decision Theory Paradoxes, Simpson's Paradox, Gambler's Fallacy, Monty Hall Problem, St. Petersburg Paradox (Paperback)

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 37. Chapters: Decision theory paradoxes, Simpson's paradox, Gambler's fallacy, Monty Hall problem, St. Petersburg paradox, Parrondo's paradox, Two envelopes problem, Three Prisoners problem, Ellsberg paradox, Decision making paradox, Proebsting's paradox, Stein's example, Exchange paradox, False positive paradox, Proof of Stein's example, Lindley's paradox, Low birth weight paradox, Berkson's paradox, Accuracy paradox, Will Rogers phenomenon, Necktie paradox, Friendship paradox, Abelson's paradox, Freedman's paradox. Excerpt: The Monty Hall problem is a probability puzzle loosely based on the American television game show Let's Make a Deal and named after the show's original host, Monty Hall. The problem, also called the Monty Hall paradox, is a veridical paradox because the result appears odd but is demonstrably true. The Monty Hall problem, in its usual interpretation, is mathematically equivalent to the earlier Three Prisoners problem, and both bear some similarity to the much older Bertrand's box paradox. The problem was originally posed in a letter by Steve Selvin to the American Statistician in 1975. (Selvin 1975a) (Selvin 1975b) A well-known statement of the problem was published in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990): Vos Savant's response was that the contestant should always switch to the other door. If the car is initially equally likely to be behind each door, a player who picks Door 1 and doesn't switch has a 1 in 3 chance of winning the car while a player who picks Door 1 and does switch has a 2 in 3 chance. Consequently, contestants who switch double their chances of winning the car. Many readers refused to believe that switching is beneficial. After the Monty Hall problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to ...