Author: Ed Schröder
Date: 06:49:00 01/09/02
Go up one level in this thread
On January 07, 2002 at 20:24:01, Hans van der Zijden wrote: >You are in a quiz and you have to choose one of three doors. Behind one of the >doors is a nice price (lets say an AMD 2000+ with all the chessprograms you >want, to make it a computerchess topic). The other doors are empty. When you >tell the quizmaster your choice he opens one of the other doors which is empty. >Now he is giving you the option to change your mind. Should you stick with your >first choice, should you change or doesn't it make a difference? > >If you don't know this riddle, try to find the solution before reading on. > >I told a friend this riddle and she is still convinced that it doesn't matter if >you change or not. She agrees that you have 1/3 chance getting it right the >first guess, but after one (empty) door is opened she keeps saying there are 2 >doors left, so now you have 1/2 chance if you stick to your choice. I try to >explain it to her in all the ways I could think of, but she is as stubborn as 3 >mules. I also played this situation 30 times with and 30 times without changing. >She thinks I was lucky and the random die showed too many times the number 1. >Anyone an idea how to explain this to her. > > >Solution: > >Suppose you choose door number 1 and you do not change. There are three >possibilities: > a. The price is behind door number 1 so you are right > b. The price is behind door number 2 so you are wrong > c. The price is behind door number 3 so you are wrong >So the chance is 1/3. > >Now a door is opened. >In situation a the quizmaster will open door 2 or 3, you don't change, you win. >In situation b the quizmaster will open door 3, you don't change, you lose. >In situation c the quizmaster will open door 2, you don't change, you lose. >So still your chance is 1/3 > >Now you are going to change. Again lets say you choose 1 and again there are >three possibilities: > a. Price is behind door 1, quizmaster opens door 2 or 3, you change, you lose. > b. Price is behind door 2, quizmaster opens door 3, you change, you win. > c. Price is behind door 3, quizmaster opens door 2, you change, you win. >So if you change you have 2/3 chance of getting the big price. > >Greetings, Hans. Wrong, it's 100%. After you are offered to change your mind, you loudly start beating your brains trying to find the best solution going through all the possibilities as decribed above. The quizmaster has no choice then to follow your thoughts while scratching his head, the audience starts to interfere, the broadcast is close to the next commercial break. No doubt the quizmaster will give you a silent hint to take the right door and hate you for that and so will your former algebra teacher. Naturally mother will be proud on her son's logic. Don't trust logic, you successfully have started to write a chess program, you should know by now that logic does not exist. The next ducth open you have 50% chance to become the new champion, you will become or you won't become. Or do you think that giving "Gadget" a second chance (game) after each lost game will increase your chances to 75%? Please take my ramblings not serious :) Ed
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