Concept

Two envelopes problem

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 interpretation of probability theory. It is a variant of an older problem known as the necktie paradox. The problem is typically introduced by formulating a hypothetical challenge like the following example: Imagine you are given two identical envelopes, 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? Since the situation is symmetric, it seems obvious that there is no point in switching envelopes. On the other hand, a simple calculation using expected values suggests the opposite conclusion, that it is always beneficial to swap envelopes, since the person stands to gain twice as much money if they switch, while the only risk is halving what they currently have. A person is given two indistinguishable envelopes, each of which contains a sum of money. One envelope contains twice as much as the other. The person may pick one envelope and keep whatever amount it contains. They pick one envelope at random but before they open it they are given the chance to take the other envelope instead. Now suppose the person reasons as follows: The puzzle is to find the flaw in the line of reasoning in the switching argument. This includes determining exactly why and under what conditions that step is not correct, to be sure not to make this mistake in a situation where the misstep may not be so obvious. In short, the problem is to solve the paradox. The puzzle is not solved by finding another way to calculate the probabilities that does not lead to a contradiction. There have been many solutions proposed, and commonly one writer proposes a solution to the problem as stated, after which another writer shows that altering the problem slightly revives the paradox.

About this result
This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.