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Auston, Brian, and Charlie each roll a fair dice simultaneously.

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Auston, Brian, and Charlie each roll a fair dice simultaneously. [#permalink]

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New post 15 Apr 2017, 04:02
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Auston, Brian, and Charlie each roll a fair dice simultaneously. The rolls of the die are independent and the outcome is thought to be random. What is the probability that exactly one of the three individuals obtains a six on his dice while the other two individuals do not?

A) 1/216
B) 25/216
C) 5/36
D) 25/72
E) 125/216
[Reveal] Spoiler: OA

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Re: Auston, Brian, and Charlie each roll a fair dice simultaneously. [#permalink]

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New post 15 Apr 2017, 06:58
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Probabilty of getting a 6 is 1/6 and not getting a six is 5/6

Lets take the probability of one case when Auston gets a six and other two do not: 1/6*5/6*5/6 = 25/216

We have three such cases so prob = 25/216*3 = 25/72

Ans D


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Auston, Brian, and Charlie each roll a fair dice simultaneously. [#permalink]

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New post 04 May 2017, 13:29
Rishirajchauhan11 wrote:
Probabilty of getting a 6 is 1/6 and not getting a six is 5/6

Lets take the probability of one case when Auston gets a six and other two do not: 1/6*5/6*5/6 = 25/216

We have three such cases so prob = 25/216*3 = 25/72

Ans D


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Don't we have more than three cases? There should be six cases where it's possible:

Abc
Acb
aBc
cBa
abC
baC

Can combinations be used to solve this problem?
Auston, Brian, and Charlie each roll a fair dice simultaneously.   [#permalink] 04 May 2017, 13:29
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Auston, Brian, and Charlie each roll a fair dice simultaneously.

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