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The Missing Link

 

Teacher-TalkMissingLink

From: David Gray (davidleroygray@hotmail.com)
Date: Tue Jun 18 2002 - 18:13:56 EDT

  • Next message: G1E2sons@aol.com: "Re: [Teacher-Talkmissinglink] oak trees and such"

    Hi. I worked on this earlier and arrived at the same solution as Gale and
    for the same reasons.

    In the process to check my probability prowess I also determined that:
         The probability that all of the salesmen were truthful is:
                    3/7 * 3/7 * 3/7 = 27/343
         The probability that all the salesmen were lying is:
                    4/7 * 4/7 * 4/7 = 64/434
         The probability that a salesmen was truthful is:
                    3/7 * 4/7 * 4/7 = 48/343 Multiply this by 3 to get the total
                    for all the possibilities of any one of the salesmen (a,b,c)
                    being the truthful one. Thus 3 * 48/343 = 144/343
         The probability that a salesmen was lying is:
                    3/7 * 3/7 * 4/7 = 36/343 Multiply this by 3 to get the total
                    for all the possibilities of any one of the salesmen (a,b,c)
                    being the liar. Thus 3 * 36/343 = 108/343
    My check for this is 27/343 + 64/343 + 144/343 + 108/343 = 343/343 = 1
    That accounts for all the possibilities.

    I always like to add extensions, extra, or what ever you choose to call work
    student can do that finished early. Here are some ideas:

    Using the same data, create another problem and solve it.
    Changing the data, solve the new problem.

    Here are other questions my mind entertains while wallowing in numbers:

    What are the odds that any of these 7 salesmen could identify an oak tree?

    What are the odds that any of these 7 salesmen would try to sell a tree of
    lesser quality than an oak as an oak tree?

    Which of the above odds do you think would be greater?

    And for a science connection: If 9/73 of the trees in a forest are oak, then
    what kind of forest might it be and where might you find such a forest?
    Assume this forest is in its climax stage.

    I must sign off before I nODDS off,

    David

    >From: Colleen Keirn <ckeirn@cfa.harvard.edu>
    >Reply-To: Teacher-Talkmissinglink@learner.org
    >To: Teacher-Talkmissinglink@learner.org
    >Subject: [Teacher-Talkmissinglink] oak trees and such
    >Date: Tue, 18 Jun 2002 16:08:45 -0400
    >
    >>At 3:04 PM -0600 6/11/02, Gale Greenlee wrote:
    >>> Hello: I wanted to discuss the various methods used to solve
    >>>the following puzzle. So to start the discussion I will present
    >>>the puzzle and then discuss the solution with anyone who is
    >>>interested. Here goes.
    >>>
    >>>
    >>>
    >>>"Salesmen lie 4/7 of the time. We pick a tree in the forest, at
    >>>random, and ask the salesmen (three of them) to tell us what kind
    >>>of a tree it is. All three agree that it is an oak. The
    >>>probability the tree is an oak is 9/73. What portion of the trees
    >>>are oaks?"
    >>>
    >>>
    >>>
    >>Gale
    >
    >Ok, I am going to take a stab at this. I have no basis, other than a
    >hunch, to base it on. I have no idea if I am right, by the way, just
    >coming at this on a Tuesday afternoon.
    >
    >My process/guess:
    >
    >The first bits of information are extraneous. The key information is
    >"The probability the tree is an oak is 9/73." That means for every
    >73 trees, 9 are oaks. So my guess is 9/73rds of the trees are oaks.
    >
    >Just a thought. I'm really interested in this question now!
    >
    >--Colleen
    >
    >--
    >-*-*-*-*-*-*-*-*-*-*-*-*-*-
    >
    >Colleen Keirn
    >Workshop Coordinator
    >
    >The Annenberg Channel
    >c/o Harvard-Smithsonian Center for Astrophysics
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    >Cambridge, MA 02138 USA
    >
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    >Email: ckeirn@cfa.harvard.edu / channel@learner.org
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