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ThomasBerger Special user 593 Posts |
I just finished reading "A mathematician plays the market" by John Allen Paulos.
It's a book about maths and the stock market. But there was an interesting little bit that might be able to be used by someone in some application or routine. It's an example of probability theory being counter-intuitive. You have 3 cards. One is red on both sides. One is black on both sides. One is red on one side, black on the other. Obviously you could use paper with O and X's or whatever. Spectator (sucker) shuffles them up any which way, turning any of them over randomly. One card is brought out. Say its red. The idea is to guess what is on the other side. Obviously its not the black/black one. So is it red/red or red/black? If you were in a pub, you would bet a beer that the other side was red too. In other words, you are saying its the red/red card. Spectator wins if it's black on the other side. At first glance this looks 50/50. But its not...you are right 2 out of 3 times. You can't lose in the long run. Why is it so? The reason you win is because there are 2 ways you can win, and one way for the spec to win. The card the spec brings out shows red...if it's black on the other side the spec wins. But it could be one side of the red/red card (you win) or the other side of the red/red card where you also win. Thus you have a 2/3 chance of getting it right. Not sure if something can be made of this, but it is so counter-intuitive (most people swear its 50-50), I thought I would post it. Cheers. Tom |
kinesis Inner circle Scotland, surrounded by 2708 Posts |
I find this theory fascinating. There are several demo's online that also explain the theory in lay terms. Try this site.
http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html Enjoy |
PaulEverson Regular user 137 Posts |
That's a little like the one with the goat and the doors..
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Joshua Quinn Inner circle with an outer triangle 2054 Posts |
Quote:
On 2004-12-16 06:28, PaulEverson wrote: A.K.A. the "Monty Hall Problem." Here's another great site that not only lets you demonstrate the effect yourself, but also lets you run a set number of trials either changing your original choice or not (so you can see the effect without all that tedious clicking): http://www.grand-illusions.com/simulator/montysim.htm
Every problem contains the seeds of its own solution. Unfortunately every problem also contains the seeds of an infinite number of non-solutions, so that first part really isn't super helpful.
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drwilson Inner circle Bar Harbor, ME 2191 Posts |
So here's a web site that links to other web sites on the Monty Hall problem:
http://math.rice.edu/~pcmi/mathlinks/montyurl.html Yours, Paul |
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