[extropy-chat] three coins in a fountain

spike spike66 at comcast.net
Thu Oct 20 19:06:25 UTC 2005

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.


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