Two envelopes problem: Difference between revisions

Revision as of 21:32, 25 June 2023

Revision as of 03:37, 26 June 2023

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[[File:Two envelopes.svg|thumb|The problem concerns two envelopes, each containing an unknown amount of money]]

The '''two envelopes problem''', also known as the '''exchange paradox''', is a [[paradox]] in [[probability theory]]. It is of special interest in [[decision theory]], and for the [[Bayesian probability|Bayesian interpretation]] of [[probability|probability theory]]. It is a variant of an older problem known as the [[necktie paradox]].

The problem is typically introduced by formulating a [[Hypothesis|hypothetical]] challenge like the following example:

{{Cquote|Imagine you are given two identical [[envelope]]s, each containing money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope at will, but before inspecting it, you are given the chance to switch envelopes. Should you switch?