From: David Gray (davidleroygray@hotmail.com)
Date: Tue Jun 18 2002 - 18:13:56 EDT
Next message: G1E2sons@aol.com: "Re: [Channel-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: channel-talkmissinglink@learner.org
>To: channel-talkmissinglink@learner.org
>Subject: [Channel-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
>60 Garden Street - MS 82
>Cambridge, MA 02138 USA
>
>Phone: 617-496-7686 / 800-228-8030 x1
>Fax: 617-496-7670
>Email: ckeirn@cfa.harvard.edu / channel@learner.org
>URL: http://www.learner.org
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