Author: John Merlino
Date: 12:06:58 09/25/02
Go up one level in this thread
On September 25, 2002 at 12:38:06, Rolf Tueschen wrote: >Please take a look at my revolutionary solution of this confusing problem: > >http://hometown.aol.de/rolftueschen/monty.html > > >At first I went into the net and collected all sort of data for my page. I >wanted to show how important methods and methodology are for science and also >statistics. In special the exact defining of the terms. > >Then suddenly I had the inspiration and in a few minutes whitewashed a million >people who as pupils, students or even professors let them be proved wrong by >Marilyn vos Savant who has an IQ of 228. For decades now the Monty Hall Problem >is taken as example for conditioned probability, which is wrong! > >Hope you enjoy my revelations. Please tell me if you want to comment. > >Rolf Tueschen You are incorrect. The problem AS STATED gives a 2/3 probability of being correct if you switch. The "host" has nothing to do with it, because he/she MUST choose a door to open. The REAL Monty Hall, IIRC, commented on this problem and he stated that this problem did NOT mimic the actual event on the "Let's Make a Deal" game show. On the show, he had a CHOICE of whether or not to open a door, meaning that, regardless of whether or not a door was opened, the probability of being correct was always 1/3. I also believe that vos Savant later commented on this variation as well. However, in this problem, a door MUST be opened, and therefore the chances of being correct are 2/3. This is simple to simulate, and it is a very common problem in beginning programming courses. Here is the output from my version: Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 2, Picked 1, Showed 0, Switched to 2, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 1, Showed 0, Switched to 2, GOAT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 2, Picked 2, Showed 0, Switched to 1, GOAT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! Cadillac in 1, Picked 2, Showed 0, Switched to 1, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 0, Picked 0, Showed 1, Switched to 2, GOAT! Cadillac in 0, Picked 2, Showed 1, Switched to 0, CORRECT! Cadillac in 1, Picked 0, Showed 2, Switched to 1, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 0, Picked 1, Showed 2, Switched to 0, CORRECT! Cadillac in 2, Picked 0, Showed 1, Switched to 2, CORRECT! 71 out of 100 times was correct when switching Running it five more times resulted in 68, 68, 66, 64 and 69. Obviously 2/3 over the long haul. Basically, it boils down to the only time you lose is if you initially chose correctly, which has a probability of 1/3. Therefore, the winning probability is 2/3. jm
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