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Offline Builderboy

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Probability Puzzle
« on: September 27, 2011, 07:57:23 pm »
I have two coins in my hand.  I flip both of them secretly until I get a result that is not two tails.  I then turn to you and show you that one of the coins is heads, and ask what the probability of the other being heads.
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Offline yunhua98

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Re: Probability Puzzle
« Reply #1 on: September 27, 2011, 08:44:28 pm »
Spoiler For answer:
1/3
« Last Edit: September 27, 2011, 08:44:42 pm by yunhua98 »
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Offline Builderboy

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Re: Probability Puzzle
« Reply #2 on: September 27, 2011, 08:45:54 pm »
Indeed :] Most people take the intuitive result, which is wrong in this case, which is why I like this puzzle so much ^^
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Offline yunhua98

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Re: Probability Puzzle
« Reply #3 on: September 27, 2011, 08:47:38 pm »
I actually know the answer because of the Monty Hall Problem with Marilyn Vos Savant.
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To paraphrase Oedipus, Hamlet, Lear, and all those guys, "I wish I had known this some time ago."
Signature Last Updated: 12/26/11
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Offline Builderboy

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Re: Probability Puzzle
« Reply #4 on: September 27, 2011, 08:49:05 pm »
Ah yes!  I just now realized the problems are equivalent!  I actually derived this from a separate problem about two children, but now i see how similar it is to the monty hall problem ^^
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Offline LincolnB

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Re: Probability Puzzle
« Reply #5 on: September 27, 2011, 09:23:24 pm »
I think I understand how this works, would you mind explaining step by step?
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Offline yunhua98

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Re: Probability Puzzle
« Reply #6 on: September 27, 2011, 09:26:30 pm »
Okay, there are three possible arrangements for the coins, given that it's not two tails: HH, TH, HT
since one of them is heads, the other can be a hh, th, or ht.  The probability where the remaining letter is a heads is one out of three.
« Last Edit: September 27, 2011, 09:27:59 pm by yunhua98 »
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To paraphrase Oedipus, Hamlet, Lear, and all those guys, "I wish I had known this some time ago."
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Offline LincolnB

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Re: Probability Puzzle
« Reply #7 on: September 27, 2011, 10:38:39 pm »
Oh, I get it, because it would be a two thirds chance that the other coin is tails.
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Offline Deep Toaster

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Re: Probability Puzzle
« Reply #8 on: September 28, 2011, 12:20:11 am »
That's not intuitive at all ... whoa :o
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