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• wysper5, your question is a really difficult one, because it s not a mathematical question, it s a modelling question. How do you mathematically represent the
Message 1 of 5 , Mar 4, 2002
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wysper5, your question is a really difficult one, because it's not
a mathematical question, it's a modelling question.

How do you mathematically represent the experiment you do when you
throw a single die three times ? The usual representation is the
set of all (x,y,z) in {1,2,3,4,5,6}^3 with equiprobability on this set.
Here, x is an integer representing the result of the first throw,
y an integer representing the result of the second one, and z an
integer representing the result of the third one.
And equiprobability means that every result (x,y,z) has the same
probability, that is probability 1/6^3 because there are 6^3
differents results (x,y,z).

With this representation, the probability of throwing no "6" at all
is (5/6)^3 (with equiprobability, x,y and z are independant random
variables and each one has a prob. 5/6 of not being "6").
Thus the probability of throwing a "6" at least once is 1-(5/6)^3.

Now how do you mathematically represent the experiment you do when you
throw three dice at one time ? Again, the usual representation
is the set of all (x,y,z) in {1,2,3,4,5,6}^3 with equiprobability.
Now x represents the result of the red die, y represents the result
of the blue die, and z represents the result of the green die
(the colors are of no importance, but it's easier to understand the
representation if you think the dice have different colors).

The representation being the same as before, the probability of the
event "6 at least once" will also be the same: 1-(5/6)^3.

But these representations are only the usual ones.
You are completely free to choose another one if you want to.
Well, if it is really different, it will probably not work,
in the sense that it will not correctly predict what happens
if you repeat the experiment 1000 times.
But nobody will be able to prove that your modelling is "mathematically
false", because modelling is what you do just before you begin doing maths.

So there is no mathematical answer to your question
"is the prob. of throwing a "6" at least once the same if you throw
a single die three times and if u throw three dice at one time?"
It depends on the representations you choose for both experiments.
The only answer I can give you is a partial answer:
With the above (usual) representations, yes, the prob. is the same.
• ... Here is an example of representation where the probability would not be the same: Suppose you are in a Casino where all dice are so strongly biased that
Message 2 of 5 , Mar 4, 2002
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> It depends on the representations you choose for both experiments.
> The only answer I can give you is a partial answer:
> With the above (usual) representations, yes, the prob. is the same.

Here is an example of "representation" where the probability would
not be the same: Suppose you are in a Casino where all dice are so
strongly biased that they always come up with the same outcome, e.g.
die number 1. always plays a 5, die number 2 always a 3 etc...
Suppose furthermore that the casino has an equal number of dice with
a 1,2,3,4,5, and 6 bias, and that you randomly pick your dice from a
big box with an (almost) infinite number of dice....

If you throw the same die three times, the probability of getting 6
at least once is 1/6 (You either get 6 three times or never)

If you pick three dice that you throw once, the probability of
getting 6 at least once is 1-(5/6)^3. [Not exactly if you have a
finite number of dice in the casino...]

Regards. Noel.
• 3 red and 4 blue balls are in a basket. A member of PPTeam is drawing balls from the basket. What is the probablity of getting the 3 red balls simultaneously?
Message 3 of 5 , Aug 30, 2006
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3 red and 4 blue balls are in a basket. A member of PPTeam is drawing
balls from the basket. What is the probablity of getting the 3 red
balls simultaneously?
• ... one out of 35
Message 4 of 5 , Aug 30, 2006
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--- In probability@yahoogroups.com, "Suresh Kumar V.S"
<suresh1983kvs@...> wrote:
>
> 3 red and 4 blue balls are in a basket. A member of PPTeam is drawing
> balls from the basket. What is the probablity of getting the 3 red
> balls simultaneously?
>
one out of 35
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