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Topic: interesting probability problem
Replies: 9   Last Post: Oct 17, 2007 3:20 AM

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Posts: 130
Registered: 5/22/05
Re: interesting probability problem
Posted: Oct 17, 2007 3:20 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply wrote:

> To glean any information about cows we need to observe an object from
> a sample space that might include cows. I think it all comes down to
> how you interpret "we make an observation of a cow or a crow, with
> probability q and 1-q". I read it as meaning that with probability q
> we go cow-observing, and with probability 1-q we go crow-observing. If
> we go crow-observing then, conceptually, we choose a crow at random
> from the set of all crows. This set can't possibly contain any cows of
> any colour, so our observation can't tell us anything about cows
> (irrespective of whether we already know that all crows are black).
> Different interpretations of this statement might lead to different
> answers: it's essential to explain unambiguously exactly what
> observing procedure is to be followed, which IMO the author has not
> done.

I now see it. You are completely right. I was being sloppy about the
intrepretation of the contrapositive of the statement that all cows are
white. To support the contrapositive, just like we could find evidence
to support the statement A, we would need to pick a random non-white
object, and then check whether it is a cow or not, which is what you
have been saying all along. Thnx.

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