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#1 2011-06-01 19:55:54
- bobcatfans
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Flaws in logic of solution to a couple of the logic problems
The solution given for the problem of the white and black marbles is flawed. We are dealing with combinations here and not permutations. Once a white marble is drawn, it doesn't matter if it was the first or second marble. There are only two possible outcomes at this point and therefore the probability is one in two.
The solution for the problem of the goats and new car is similarly flawed. At the point that the one goat is shown, there are only two possibilities remaining. Changing your pick will NOT increase your probability of winning the car. The probability of your original pick DOES change once the one door is opened! 
#2 2011-06-01 21:42:39
- bobbym
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Re: Flaws in logic of solution to a couple of the logic problems
Hi bobcatfans;
Welcome to the forum.
If you are referring to the Monty Hall problem then switching is definitely favorable. Just tree the problem.
A long time ago Marilyn Vos Savant made a big stir when she caught a bunch of people making a mistake on this problem. The problem first pops up in a statistics journal circa 1958.
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#3 2011-06-14 18:58:15
- Anne Smith
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Re: Flaws in logic of solution to a couple of the logic problems
I quite agree with your last member. The options are only that it is a white or a black marble, because whether or not you have already selected marble 1 or two from bag A the next outcome is a white anyway.
#4 2011-06-14 19:29:30
- bobbym
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Re: Flaws in logic of solution to a couple of the logic problems
Hi Anne Smith;
Welcome to the forum!
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#5 2011-06-14 22:32:19
- MathsIsFun
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Re: Flaws in logic of solution to a couple of the logic problems
Are you referring to this: Bags of Marbles - Solution ?
"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman
#6 2012-07-25 21:57:17
- Nicholas
- Guest
Re: Flaws in logic of solution to a couple of the logic problems
I agree this answer is wrong it says the answer is 2/3 because you are picking marbles not bags. That answer is if you were picking bags. The probability of you picking a white marble is 3/6 or simplified 1/2.
You have the wrong answer posted.
#7 2012-07-25 22:17:23
- bob bundy
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Re: Flaws in logic of solution to a couple of the logic problems
hi Nicholas,
Welcome to the forum!
Do you have a method for generating random events with known probabilities (eg. Excel) ?
If so, then try simulating this a large number of times. Maybe it will help to change your mind. 
Or study Bayes Theorem and probability tree diagrams.
Bob
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#8 2012-07-25 23:03:30
- anonimnystefy
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Re: Flaws in logic of solution to a couple of the logic problems
The problem is called Bertrand's box paradox.
There is another neat solution on wikipedia.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#9 2012-07-25 23:19:20
- noelevans
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Re: Flaws in logic of solution to a couple of the logic problems
Does the original problem state that the marbles are distinguishable or not?
Distinguishability makes a big difference in the way probabilities turn out. Could it be that the 1/2 comes from indistinguishability and the 2/3 from distinuishability? The solution in post #5 appears to assume distinguishability.
Some other important concerns in probability: Repetition vs not, replacement vs not, the sample space for the problem. Probability can be exceedingly tricky!
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
#10 2012-07-25 23:32:19
- anonimnystefy
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Re: Flaws in logic of solution to a couple of the logic problems
I think the probability stays the same in both cases. Did you look at the Wikipeadia article on the Bertrand's box paradox.
The limit operator is just an excuse for doing something you know you can't.
“It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman
“A secret's worth depends on the people from whom it must be kept.” ― Carlos Ruiz Zafón
#11 2012-07-26 04:25:33
- noelevans
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Re: Flaws in logic of solution to a couple of the logic problems
Yup! I looked at the Wiki article. But alas I haven't had time to really think about it all. I'm helping a friend move most of today.
Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).
LaTex is like painting on many strips of paper and then stacking them to see what picture they make.
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