Let us say the two mugs both contain M [your fav unit of measure] of
milk/coffee.
Let us assume the spoon contains S.
M1 M2
M cof M milk
1) You take one teaspoon of Milk from Mug Two and stir it thoroughly into the
Coffee in Mug One: situation:
M1 M2
M cof + S milk M-S milk
2) You then take one teaspoon of the liquid from Mug One and put it into Mug
Two.
What you take from mug one is S liquid, which is, in percent:
S/(M+S) milk
M/(M+S) cof
so what you are taking out of M1 is:
S*(S/(M+S)) milk
S*(M/(M+S)) coffee
this leads to:
M1: M-S*(M/(M+S)) cof ; S-S*(S/(M+S)) milk
M2: M-S+S*(S/(M+S)) milk ; S*(M/(M+S)) coffee
let's compare coffee in M1 versus milk in M2:
M-S*(M/(M+S)) coffee in M1;
M-S+S*(S/(M+S)) milk in M2
this can be transformed as follows:
[M(M+S)-SM] / (M+S) coffee in M1;
[M(M+S)-S(M+S)+S^2] / (M+S) milk in M2.
we can eliminate / (M+S) since it appears in both expressions (and we want to
compare them). Also perform multiplications:
M^2 + MS - SM = M^2 coffee in M1
M^2 + MS - SM - S^2 + S^2] = M^2 milk in M2
EQUAL!
both contain M^2/(M+S) of their original liquid.
Give me another one! :)
AS
Lawrence DeBivort ha scritto:
> In honor of Jonathon and my earlier discussion of the Israeli-Palestinian
> conflict, I offer you this puzzle:
>
> You have two mugs, equal in volume. Mug One is nearly filled with Coffee.
> Mug Two is nearly filled with Milk. The volume of the milk equals that of
> the coffee.
>
> Do you end up with more Coffee in Mug Two than Milk in Mug One, or vice
> versa?
>
> Have fun.
>
> Lawry
>
> > -----Original Message-----
> > From: owner-moq_discuss@venus.co.uk
> > [mailto:owner-moq_discuss@venus.co.uk]On Behalf Of Jonathan B. Marder
> > Sent: Thursday, July 11, 2002 8:25 AM
> > To: moq_discuss@moq.org
> > Subject: RE: MD Let's Make a Deal
> >
> >
> > Hi Rick, Erin, Glenn,
> >
> > I've been in a discussion on this before. The fact that Monty provides
> > new information DOES change the statistics. You now know that door #1 is
> > worthless, so the stats are as they would be if you knew that in the
> > first place - it's 50/50 on door #2 vs. #3.
> >
> > The interesting thing about the previous debate I saw on this was that
> > nobody could agree on the solution . . . until someone ran a simulation
> > and confirmed empirically that the chance of guessing right is indeed
> > 50%. So much for theory!
> >
> > Jonathan
> >
> >
> > ---Original message from Rick [VALENCE] ---
> >
> > Here's the Setup:
> > Imagine you're a contestant on Let's Make a Deal. Monty Hall calls
> > you up to the stage and explains the game to you. He tells you there
> > are three doors. Door #1. Door #2. And Door #3. Behind two of the
> > doors (he won't tell you which of course) are worthless gag prizes, but
> > behind the third is a valuable prize (for this group, we'll imagine it's
> > an unlimited one-on-one Q&A with Robert Pirsig as he sails you down the
> > Hudson River on the Arźte).
> > Monty asks you choose a door... you pick door #2. Monty says, "Well
> > it's a good thing you didn't pick door#1." Door#1 opens and you see one
> > of the gag prizes revealed (let's say... a goat in a wheelbarrow).
> > Now you're down to your chosen door (door#2) and the remaining door
> > (door#3). Monty says, "I'll give you $100 to switch to door#3.... I'll
> > give to $200...$300...etc...etc."
> >
> > Here's the Question:
> > Does switching doors improve your odds of winning?
> >
> > Here's the Possibilities:
> > 1. Switching won't help. It's a 50/50 chance. Door #2 or Door #3.
> > Switching don't mean diddley.
> >
> > 2. Switching will help. You started with 3 doors. 2 bad and 1 good.
> > Odds are, you picked a bad one to begin with. So odds are, if you
> > switch, you're switching to a good one.
> >
> >
> >
> > Can anyone crack this one for me? Does switching improve the odds?
> >
> >
> > thanks,
> > rick
> >
> >
> >
> > MOQ.ORG - http://www.moq.org
> > Mail Archive - http://alt.venus.co.uk/hypermail/moq_discuss/
> > MD Queries - horse@darkstar.uk.net
> >
> > To unsubscribe from moq_discuss follow the instructions at:
> > http://www.moq.org/md/subscribe.html
> >
>
> MOQ.ORG - http://www.moq.org
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>
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