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- Two_envelopes_problem abstract "The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle, or paradox in logic, philosophy, probability, and recreational mathematics. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. Historically, it arose as a variant of the necktie paradox.The problem:You have two indistinguishable envelopes that each contain money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. You pick at random, but before you open the envelope, you are offered the chance to take the other envelope instead.It can be argued that it is to your advantage to swap envelopes by showing that your expected return on swapping exceeds the sum in your envelope. This leads to the paradoxical conclusion that it is beneficial to continue to swap envelopes indefinitely.ExampleAssume the amount in a selected envelope is $20. If the envelope happens to be the larger of the two envelopes ("larger" meaning the one with the larger amount of money), that would mean that the amount in the envelope is twice the amount in the other envelope. So in this case the amount in the other envelope would be $10.However if the selected envelope is the smaller of the two envelopes, that would mean that the amount in the other envelope is twice the amount in the selected envelope. In this second scenario the amount in the other envelope would be $40.The probability of either of these scenarios is one half, since there is a 50% chance that the larger envelope was selected and a 50% chance that the smaller envelope was selected. The expected value calculation for how much money is in the other envelope would be the amount in the first scenario times the probability of the first scenario plus the amount in the second scenario times the probability of the second scenario, which is $10 * 1/2 + $40 * 1/2. The result of this calculation is that the expected value of money in the other envelope is $25. Since this is greater than the selected envelope, it would appear to the person selecting the envelope's advantage to always switch envelopes.A large number of solutions have been proposed. The usual scenario is that one writer proposes a solution that solves the problem as stated, but then another writer discovers that altering the problem slightly revives the paradox. In this way, a family of closely related formulations of the problem have been created, which are discussed in the literature.No proposed solution is widely accepted as correct. Despite this it is common for authors to claim that the solution to the problem is easy, even elementary. However, when investigating these elementary solutions they often differ from one author to the next. Since 1987 new papers have been published every year.".
- Two_envelopes_problem thumbnail Envelop.jpg?width=300.
- Two_envelopes_problem wikiPageID "2539764".
- Two_envelopes_problem wikiPageRevisionID "606400866".
- Two_envelopes_problem hasPhotoCollection Two_envelopes_problem.
- Two_envelopes_problem subject Category:Decision_theory_paradoxes.
- Two_envelopes_problem subject Category:Named_probability_problems.
- Two_envelopes_problem subject Category:Probability_theory_paradoxes.
- Two_envelopes_problem type Abstraction100002137.
- Two_envelopes_problem type Attribute100024264.
- Two_envelopes_problem type Communication100033020.
- Two_envelopes_problem type Condition113920835.
- Two_envelopes_problem type Contradiction107206887.
- Two_envelopes_problem type DecisionTheoryParadoxes.
- Two_envelopes_problem type Difficulty114408086.
- Two_envelopes_problem type Falsehood106756407.
- Two_envelopes_problem type Message106598915.
- Two_envelopes_problem type NamedProbabilityProblems.
- Two_envelopes_problem type Paradox106724559.
- Two_envelopes_problem type ProbabilityTheoryParadoxes.
- Two_envelopes_problem type Problem114410605.
- Two_envelopes_problem type State100024720.
- Two_envelopes_problem type Statement106722453.
- Two_envelopes_problem comment "The two envelopes problem, also known as the exchange paradox, is a brain teaser, puzzle, or paradox in logic, philosophy, probability, and recreational mathematics. It is of special interest in decision theory, and for the Bayesian interpretation of probability theory. Historically, it arose as a variant of the necktie paradox.The problem:You have two indistinguishable envelopes that each contain money. One contains twice as much as the other.".
- Two_envelopes_problem label "Enveloppenparadox".
- Two_envelopes_problem label "Paradoja de los dos sobres".
- Two_envelopes_problem label "Paradosso delle due buste".
- Two_envelopes_problem label "Paradoxe des deux enveloppes".
- Two_envelopes_problem label "Two envelopes problem".
- Two_envelopes_problem label "Umtauschparadoxon".
- Two_envelopes_problem label "Задача о двух конвертах".
- Two_envelopes_problem label "钱包悖论".
- Two_envelopes_problem sameAs Paradox_dvou_obálek.
- Two_envelopes_problem sameAs Umtauschparadoxon.
- Two_envelopes_problem sameAs Paradoja_de_los_dos_sobres.
- Two_envelopes_problem sameAs Paradoxe_des_deux_enveloppes.
- Two_envelopes_problem sameAs Paradosso_delle_due_buste.
- Two_envelopes_problem sameAs Enveloppenparadox.
- Two_envelopes_problem sameAs m.07lvb4.
- Two_envelopes_problem sameAs Q180191.
- Two_envelopes_problem sameAs Q180191.
- Two_envelopes_problem sameAs Two_envelopes_problem.
- Two_envelopes_problem wasDerivedFrom Two_envelopes_problem?oldid=606400866.
- Two_envelopes_problem depiction Envelop.jpg.
- Two_envelopes_problem isPrimaryTopicOf Two_envelopes_problem.
