# Omnimaga

## General Discussion => Other Discussions => Miscellaneous => Topic started by: Builderboy on September 27, 2011, 07:57:23 pm

Title: Probability Puzzle
Post by: Builderboy 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.
Title: Re: Probability Puzzle
Post by: yunhua98 on September 27, 2011, 08:44:28 pm
1/3
Title: Re: Probability Puzzle
Post by: Builderboy 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 ^^
Title: Re: Probability Puzzle
Post by: yunhua98 on September 27, 2011, 08:47:38 pm
I actually know the answer because of the Monty Hall Problem with Marilyn Vos Savant.
Title: Re: Probability Puzzle
Post by: Builderboy 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 ^^
Title: Re: Probability Puzzle
Post by: LincolnB on September 27, 2011, 09:23:24 pm
I think I understand how this works, would you mind explaining step by step?
Title: Re: Probability Puzzle
Post by: yunhua98 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.
Title: Re: Probability Puzzle
Post by: LincolnB 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.
Title: Re: Probability Puzzle
Post by: Deep Toaster on September 28, 2011, 12:20:11 am
That's not intuitive at all ... whoa :o