# [extropy-chat] three coins in a fountain

Brandon Reinhart transcend at extropica.com
Fri Oct 21 05:17:27 UTC 2005

```> What is the probability that the other side is a tail?

This sounds like a problem for Bayes Theorem.

p(A|X) = p(X|A) * p(A) / ( p(X|A)*p(A) + p(X|~A)*p(~A) )

Coins: H/H, T/T, H/T

A - The bottom is a tail.
X - The top is a head.

p(A|X) = The probability that the bottom of the coin is a tail, when the top

p(A) - Prior probability (likelihood with no new information) that the
bottom of any coin drawn will be a tail: 50% (there are 6 sides total, 3

P(~A) - Prior probability that the bottom of any coin drawn will be a head:
50%.

p(X|A) - 33% of coins with a bottom tail will have a top head.

p(X|~A) - 33% of coins with a bottom not a tail will have a top head.

P(A|X) = 33% * 50% / ( 33%*50% + 33%*50% ) = 0.165 / ( 0.165 + 0.165 ) =
0.165 / 0.33 = 0.5

The likelihood that the coin drawn has a tail on the other side is 50%. In
fact, the information we are given (that we see a head) doesn't help us at
all. It is completely irrelevant information (as far as probability is
concerned).

Brandon

-----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.

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