Propeller Head Plaza Technical and scientific discussion of amps, cables and other topics.

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here is your logical fallacy

Posted by tunenut (A) on October 26, 2006 at 10:07:27

In Reply to: Re: I guess I will have to quit posted by Don T on October 26, 2006 at 08:25:01:

Thank you. I understand your nomenclature now.

"we can see there are 6 possible revelations of which only two of them can possibly indicate a winning door." TRUE

You are almost correct. But the next statement is flat out wrong:

"However since there is only one winning door only one of the winRX states actually represents the winning door."

This is not how one does a probability calculation. You need to count ALL possibilities. There is only one choice, this is true. But there are two eqaully probable possibilities.

This is why I proposed the coin problem. You need to count states and assign probabilities to each state. The fact that you only make one choice is not relevant to the number of states.

OK to get gory (it's almost Halloween after all), here we go:

PRIZE UNDER X:

1. Choose X, Monty reveals Y win by sticking
2. Choose X, Monty reveals Z, win by sticking
3. Choose Y, Monty reveals X, game over lose
4. Choose Y, Monty reveals Z, win by switching
5. Choose Z, Monty reveals X, game over lose
6. Choose Z, Monty reveals Y, win by switching

PRIZE UNDER Y:

7. Choose X, Monty reveals Y, game over lose
8. Choose X, Monty reveals Z, win by switching
9. Choose Y, Monty reveals X, win by sticking
10. Choose Y, Monty reveals Z, win by sticking
11. Choose Z, Monty reveals X, win by switching
12. Choose Z, Monty reveals Y, game over lose

PRIZE UNDER Z:

13. Choose X, Monty reveals Y, win by switching
14. Choose X, Monty reveals Z, game over lose
16. Choose Y, Monty reveals X, win by switching
16. Choose Y, Monty reveals Z, game over lose
17. Choose Z, Monty reveals X, win by sticking
18. Choose Z, Monty reveals Y, win by sticking

OK here are my 3 contentions along with questions to you:

1. I contend these 18 ways to get from start to finish are complete. Do you have a way to get from start to finish that is not on this list?

2. I contend that each of these 18 ways is possible. Do you have any on the list that you would suggest should not be on the list?

3. IMPORTANT: I contend that each of these 18 ways are EQUALLY probable. Do you have some reason why this is not the case?

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