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While playing a certain dice game, Chris wins if the sum of

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Joined: 11 Aug 2011
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Location: United States
Concentration: Economics, Finance
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While playing a certain dice game, Chris wins if the sum of [#permalink] New post 10 Aug 2014, 02:58
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Question Stats:

60% (02:10) correct 40% (02:02) wrong based on 65 sessions
While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?

A. 1/2
B. 17/36
C. 91/216
D. 11/36
E. 25/216

I could not understand how to approach this problem.
Can someone throw some light on how to solve this.
[Reveal] Spoiler: OA
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Re: While playing a certain dice game, Chris wins if the sum of [#permalink] New post 10 Aug 2014, 06:46
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There are 36 ways that a pair of dice can land. To have a sum of 7, there are 6 ways: 1-6, 2-5, 3-4, 4-3, 5-2 and 6-1

Therefore, the chance to have a sum of 7 is \frac{1}{6}.

Making a sum of 7 on the first time is \frac{1}{6}=\frac{36}{216}
Making a sum of 7 on the second time is \frac{5}{6}*\frac{1}{6}=\frac{5}{36}=\frac{30}{216}
Making a sum of 7 on the third time is \frac{5}{6}*\frac{5}{6}*\frac{1}{6}=\frac{25}{216}

Add them all together to get \frac{91}{216}

Answer is C.
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While playing a certain dice game, Chris wins if the sum of [#permalink] New post 12 Aug 2014, 05:56
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Total outcomes possible: 36
Total outcomes possible with sum 7: 6
Probability to win when rolled once = 6/36
Probability not to win when rolled once = 30/36 = 5/6
Probability to win in three attempts= 1- Probability will not to win in all three attempts
= 1- (5/6* 5/6*5/6)
= 91/216
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Re: While playing a certain dice game, Chris wins if the sum of [#permalink] New post 16 Aug 2014, 13:54
akhil911 wrote:
While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?

A. 1/2
B. 17/36
C. 91/216
D. 11/36
E. 25/216

I could not understand how to approach this problem.
Can someone throw some light on how to solve this.


I understand the solution. But I have a meaning problem:
How many dices could be rolled (max)? Three pairs (6) or three dices (3)

I understand that he rolls the
First dice (from 1 to 6). No thing I can do.
Second dice (1 to 6) = 1/6 of chance of getting a 7.
If the sum is below 7:
Third dice (1 to 6). I dont know how to calculate! =)

My final question is: is this problem ambiguous?
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Re: While playing a certain dice game, Chris wins if the sum of [#permalink] New post 17 Aug 2014, 21:31
plaverbach wrote:
akhil911 wrote:
While playing a certain dice game, Chris wins if the sum of the two dice is 7, at which point the game is over. If the game allows Chris three rolls in an attempt to win, what is the probability that Chris will win?

A. 1/2
B. 17/36
C. 91/216
D. 11/36
E. 25/216

I could not understand how to approach this problem.
Can someone throw some light on how to solve this.


I understand the solution. But I have a meaning problem:
How many dices could be rolled (max)? Three pairs (6) or three dices (3)

I understand that he rolls the
First dice (from 1 to 6). No thing I can do.
Second dice (1 to 6) = 1/6 of chance of getting a 7.
If the sum is below 7:
Third dice (1 to 6). I dont know how to calculate! =)

My final question is: is this problem ambiguous?


I think question sould be read as follows: Charlie has three rolls with two dices each of them.
Hence every roll minimum score would be 2 (1+1) and maximum 12 (6+6).
Probability of having 7 in the first roll is 1/6 (6 out of 36).
You can follow one of the two ways explained here above. Both works.
Hope it helps.
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Concentration: Strategy, Sustainability
GMAT 1: 710 Q49 V39
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While playing a certain dice game, Chris wins if the sum of [#permalink] New post 31 Aug 2014, 23:59
Why dont be consider a 4th option where on none of the 3 rolls he gets a 7? shouldnt we be adding [5][/6]^3 to the 91/216?
While playing a certain dice game, Chris wins if the sum of   [#permalink] 31 Aug 2014, 23:59
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