Author: Hans van der Zijden
Date: 17:24:01 01/07/02
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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