The Two Envelope Problem: a Paradox or Fallacious Reasoning?

Abstract

The primary objective of this note is to revisit the two envelope problem and propose a simple resolution. It is argued that the paradox arises from the ambiguity associated with the money content $x of the chosen envelope. When X=x is observed it is not know which one of the two events, X={\theta} or X=2{\theta}, has occurred. Moreover, the money in the other envelope Y is not independent of X; when one contains {\theta} the other contains 2{\theta}. By taking these important features of the problem into account, the paradox disappears.