[extropy-chat] three coins in a fountain

Julian Assange xyz at iq.org
Sat Oct 22 00:40:42 UTC 2005


You are all wrong.

In our black bag, we have

  HH
  TT
  HT

We have drawn one of these coins at random.
 
We are then informed that one FACE of one of these coins is a head. 2/3
of the head faces are in HH, 1/3 in HT.

Now we flip our coin.  If our coin was HH the flip will reveal heads
with certainty.  If our coin was HT the flip will reveal T with
certainty.

Hence there is a 2/3 chance that the otherside of the coin will display
heads.

Bayes is no substitute for understanding.

On Fri, 21 Oct 2005 12:04:33 -0700, "Rayburn, James"
<James.Rayburn at chw.edu> said:
> I generally like to read these threads, not interject. However, I
> couldn't
> hold back.
> T/T and T/H are non-possibilities. The only possibilities are H/H, H/H,
> and
> H/T. p(X|~A)=66%
> Re-crunch you get 33%, Which is the answer I've seen in previous
> incarnations of the question. Once taken to 10,000 trials with the three
> coins. Their outcome was 33%.
> I like it here. 
> Jim
> 
> -----Original Message-----
> From: Brandon Reinhart [mailto:transcend at extropica.com]
> Sent: Thursday, October 20, 2005 10:17 PM
> To: 'ExI chat list'
> Subject: RE: [extropy-chat] three coins in a fountain
> 
> 
> > 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
> is a head.
> 
> 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
> heads, 3 tails).
> 
> 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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