Author: Eric Campos
Date: 21:53:25 01/08/02
Go up one level in this thread
Such a simple problem, yet so far from being intuitive. But when you look at the problem backwards, it becomes intuitive again. So ask your friend to look at the problem backwards: Let her find the prize by eliminating the incorrect doors. Your friend already agrees that she can pick an "empty" door 2/3 of the time. In these 2/3 cases, the quizmaster will eliminate the other "empty" door, and only the prized door will remain. We should all win this game 2/3 of the time! Once she agrees she can win this game 2/3 of the time, remind her that she did so by first selecting one door, then letting the quizmaster help, then eliminating (swapping) her first choice! Swap: correct 2/3 of the time. No Swap: correct 1/3 of the time. Eric 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.
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