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## Monty Hall Dilemma

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #3698 Fun: (2.61) Difficulty: (1.88) Category: Probability Submitted By: Mogmatt16 Corrected By: Gizzer

Suppose you are on a game show. The host puts two envelopes in front of you, telling you that one contains twice as much as the other. You select envelope A, reach inside, and there is \$200. Now, the host offers you a chance to switch whatever you picked for the other envelope. Do you?

First, you must think about this: The other envelope either contains \$400 or \$100. You have a fifty/fifty chance of either gaining \$200 or losing \$100. The odds are playing in your favor. Here is the strange part though: You would have arrived at a similar conclusion if you had picked envelope 2. Personally, I would stick with what I have because it is still a 50/50 chance of increasing your total. What you have run into is the famous two-envelope paradox. If you have any better reason for switching, leave a comment.
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