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3 questions in the tradition of Stolyar... Three fair dice

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bluefox420
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3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 08:07
3 questions in the tradition of Stolyar...

Three fair dice are rolled, what is the probability that

(1) you get 3 sixes?
(2) you DO NOT get 3 sixes?
(3) you get ATLEAST one six?



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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 08:15
in the tradition... looks great!!! nice to see it!!!
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 08:49
Quote:
(1) you get 3 sixes?


(1/6)^3

Quote:
(2) you DO NOT get 3 sixes?


1-((1/6)^3)

Quote:
(3) you get ATLEAST one six?


1-((5/6)^3)
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 09:44
Let's increase the difficulty a bit, what is the probability that

you will NOT get EXACTLY 2 sixes?
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   Updated on: 09 Dec 2003, 17:49
Quote:
Let's increase the difficulty a bit, what is the probability that

you will NOT get EXACTLY 2 sixes?


x66 (5 possibilities)
6x6 (5 possibilities)
66x (5 possibilities)


15 ways out of 6^3 to get exactly 2 sixes.

((6^3)-15)/6^3

Originally posted by stoolfi on 09 Dec 2003, 11:52.
Last edited by stoolfi on 09 Dec 2003, 17:49, edited 1 time in total.
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 15:48
Is it 25 or 15? (3 x 5)
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   09 Dec 2003, 17:48
My mistake. I edited my errant message.
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   13 Dec 2003, 02:02
bluefox420 wrote:
3 questions in the tradition of Stolyar...

Three fair dice are rolled, what is the probability that

(1) you get 3 sixes?
(2) you DO NOT get 3 sixes?
(3) you get ATLEAST one six?


Quote:
(1) you get 3 sixes?


only one way out of 216 ways => 1/216

Quote:
(2) you DO NOT get 3 sixes?


1- 1/216 =215/216

Quote:
(3) you get ATLEAST one six?
[/quote]

1- (5/6)^3 = 91/216
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   13 Dec 2003, 02:05
bluefox420 wrote:
Let's increase the difficulty a bit, what is the probability that you will NOT get EXACTLY 2 sixes?



P (Exactly two sixes) = 3 * 1/6^2 * 5/6 = 5/72


Reqd prob = 1 - 5/72 = 67/72
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   13 Dec 2003, 02:06
stoolfi wrote:
Quote:
Let's increase the difficulty a bit, what is the probability that

you will NOT get EXACTLY 2 sixes?


x66 (5 possibilities)
6x6 (5 possibilities)
66x (5 possibilities)


15 ways out of 6^3 to get exactly 2 sixes.

((6^3)-15)/6^3


:?
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   05 Jan 2004, 17:16
Hi stolyar

for the improved question you need to add getting 3 sixes to getting 1 six.

x66
6x6
66x
666

1/6^3 + 3 * 1/6 * 5/6 * 5/6
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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink] 3 questions in the tradition of Stolyar... Three fair dice   10 Jan 2004, 15:33
My bad. stoolfi is right on the improved question. Q is asking not getting exactly 2 sixes.



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Re: 3 questions in the tradition of Stolyar... Three fair dice [#permalink]
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