[extropy-chat] three coins in a fountain

[Alfio Puglisi]

It's 1/3, because in the table the last three options must be excluded 
altogether (you don't see a tail). Of the remaining three, only one has a 
tail on the other side.

Alfio

On Thu, 20 Oct 2005, Acy James Stapp wrote:

> 1/6, since there is only one side of the six sides that has a tail
> opposite.
>
> Coin  Side
> HH    H*
> HH    H*
> HT    H*
> HT    T
> TT    T
> TT    T
>
> Clearly the coin you picked is one of the two starred coins. Out of the
> three
> Options provided, only one has a tail opposite.
>
> Acy
>
> -----Original Message-----
> From: extropy-chat-bounces at lists.extropy.org
> [mailto:extropy-chat-bounces at lists.extropy.org] On Behalf Of spike
> Sent: Thursday, October 20, 2005 2:06 PM
> To: 'ExI chat list'
> Subject: [extropy-chat] three coins in a fountain
>
>
> You have a bag containing three coins: a double headed,
> a double tailed and an ordinary coin.  You reach into
> the bag without looking, take one out and place it on
> the table.  You see a head facing up.
>
> What is the probability that the other side is a tail?
>
> At first you think: simple, the probability that you chose
> the ordinary coin is one of three, so its simply 1/3.  But
> on the other hand, when you looked at the coin, you learned
> that you did not choose the double tail; that one you know
> is still in the bag.  So you chose either the double head
> or the ordinary coin, equal probability of each, so its
> fifty-fifty even bet that the other side is a tail.
>
> But you already know that the probability of picking the ordinary coin
> is 1/3, and looking at the coin did not magically change that, right?
> Perhaps you came up with a different answer than either 1/3 or 1/2.
>
> Think on this puzzle, post your answer and your reasoning,
> then stand by for part 2, which is really the punchline.
>
> spike
>
>
>
>
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