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- Xref: sparky sci.math:17626 rec.puzzles:8203
- Newsgroups: sci.math,rec.puzzles
- Path: sparky!uunet!usc!rpi!batcomputer!cornell!karr
- From: karr@cs.cornell.edu (David Karr)
- Subject: Re: Marilyn Vos Savant's error?
- Message-ID: <1993Jan4.061303.4809@cs.cornell.edu>
- Organization: Cornell Univ. CS Dept, Ithaca NY 14853
- References: <1992Dec15.052211.24395@CSD-NewsHost.Stanford.EDU> <1hvp6gINN9np@chnews.intel.com> <1992Dec31.203934.1@stsci.edu>
- Distribution: na
- Date: Mon, 4 Jan 1993 06:13:03 GMT
- Lines: 43
-
- In article <1992Dec31.203934.1@stsci.edu> zellner@stsci.edu writes:
- > A. "I have two children, and one of them is right over there."
- >[...]
- >
- >You look and see a boy. What's the chances that they are both boys?
- >Enumerate the cases:
- >
- > Boy - Boy [1]
- > Boy - Girl [2]
- > Girl- Boy [3]
- > Girl- Girl [4]
- >
- >[...] But in case A you can only rule out the
- >fourth combination, and the probability is 1/3.
-
- Bad analysis. Certainly either case 2 or case 3 might be true, but
- taking into account *all* encounters in which statement A is made and
- case 2 is true, half the time you will see a girl (assuming that which
- child is "right over there" is not correlated with birth order).
- Likewise for case 3.
-
- That is, you will encounter case 1 twice as often as either one of
- case 2 or 3, yielding P(other=boy)=1/2 overall.
-
- I assume you're just trying to rephrase the problem so that the
- encounter produces nothing other than an indicator variable for
- the condition "at least one boy," but I don't think you succeeded.
-
- >But suppose someone else looks, and says "at least one of them
- >is a head." Then the probability that BOTH are heads is 1/3.
- >If you don't believe it, try a few hundred tosses.
-
- You'd better not try this if I'm the person who gets to look. Or if
- Monty Hall is. I might choose to just say, "Nice day, isn't it," in
- all the cases where there are *not* two heads, changing your desired
- conditional probability from 1/3 to 1. (And given Monty Hall's
- response to Marilyn vos Savant, I suspect he'd do something similarly
- perverse.)
-
- -- David Karr (karr@cs.cornell.edu)
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