If you read this carefully then you could win some money, even from your own colleagues. But: do this for fun only, you will have to work together again afterwards! :-)
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The paradox "Three Doors Problem" is related to a television show in the 70's: Mothy Hall's "Let's make a deal". In this popular show, a finalist was given a choice of 3 doors of which only 1 contains the big price. Behind the other 2 doors there was nothing... After the finalist chose one of the doors, the quizmaster then revealed one "empty door" among the two doors that were not chosen. After that, the quizmaster asked if the finalist would like to switch to the other door to open. The question: What should you do? Do you open the door you initially chose or do you switch to the other unopened door before? Do the odds of winning the game increase by switching to the remaining door? |
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The intuition of most people will tell them that each of the doors will offer the same chance to win. However, this is not true! The winning-chance will increase to 66% (2/3) when choosing the other door to open.
The easiest way to explain this is as follows: The chance of picking the wrong door in the initial stage of the game is 2/3 (this part is easy to understand, right?).
If the finalist was picking the wrong door, the quizmaster must open the other empty door in the second stage of the game. So, if the finalist did switch doors before opening one, the chance will increase to 66% (after all, this 66% losing chance has been turned into a 66% winning chance now). In addition to this, don't forget that the initial winning chance was only 33%. So, if the finalist was picking the right door, the losing chance will decrease to just 33% after choosing the other door. OK, this is more difficult to see...
You still don't see how it works...? Well, get 3 cups and 1 coin and simulate the game 100 times, or more.
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Here you can download a program to simplify the simulation. You can configure the application to run (for example) 1,000 times in just a few minutes. To see what happens the program is foreseen with a delay. Request: if you download the program, please send me an E-mail in order to inform me about it. Don't worry, I won't send you Spam or other boring messages, and the program is free to download, use, copy, destroy, ... |
If you like these kind of puzzles, then you should take a look at The Grey Labyrinth. However, as mentioned before, you can also find many other websites that describe the so-called "Three Doors Problem". Just click the link here or use your own favorite search engine to find out.
