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# Five fair dice with faces marked 1,2,3,4,5 and 6 are rolled.

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Senior Manager
Joined: 19 Oct 2004
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Five fair dice with faces marked 1,2,3,4,5 and 6 are rolled. [#permalink]  08 Nov 2004, 13:03
Five fair dice with faces marked 1,2,3,4,5 and 6 are rolled. Calculate the probability of throwing exactly the same number on at least four dice.

I liked this question quite a lot. Wanted to share it with everyone..
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Director
Joined: 16 Jun 2004
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Denomiator = 6^5 = 7776 possibilities.

Now, for the numerator = total outcomes(which is 6^5) - number of outcomes where all four dice show different numbers (which is 6*5*4*3) -number of outcomes where all show same number (which is 6) = 7776-360 -6 = 7410

Prob is 7410/7776 = 3705/3888. I dont think I am sure of this one. OA pls.
Senior Manager
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Well thats wrong..... Shall I give out the OA so fast?
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Director
Joined: 16 Jun 2004
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Kudos [?]: 18 [0], given: 0

I know that the numbers are getting unfriednly...some mistake...how about 5 answer choices..
Director
Joined: 16 Jun 2004
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Kudos [?]: 18 [0], given: 0

Also, missed on 'ATleast'...anyway give the answer choices...this is a tough one..
GMAT Club Legend
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Wait, not yet. I'm currently working on a report. I'll give an answer within next 15 minutes
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Paul

Senior Manager
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No answer choices for this one.. sorry venksune..

Its just a Probability sum a like. So I picked it up. IT has a few concepts in it. Lets wait for Paul's Answer.
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Director
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First draft with Bernoulli, 6.(5C4.(1/6)^4.(5/6)^1+1/6^5)=26/1296
does not smell so good

Last edited by twixt on 08 Nov 2004, 15:56, edited 3 times in total.
Director
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In the count of three I need either the answer or Paul's response...can't sleep otherwise peacefully..
GMAT Club Legend
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Kudos [?]: 209 [0], given: 0

Too late, damn report!
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Paul

Intern
Joined: 08 Nov 2004
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The probability of getting four dice to have the same number:

6 / 6^4

So, In the numerator we have: (6/6^4).6= 1/6^2

In the denominator we have 6^5

The result is: (1/6^2)/6^5 = 1/6^7
GMAT Club Legend
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Answer should be 25/7776 after the afore mentioned calculations
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Paul

Manager
Joined: 07 Nov 2004
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The probability of obtaining at least four "sixes" when rolling five dice is as per Paul's solution that is, C(5,4)*5/(6^5). However, there are six marks on each dice {1,2,3,4,5,6} so that ans is

6*C(5,4)*5/(6^5) = 5*5/(6^4) = 25/1296

My humble opinion
Manager
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Forgot the fact that all five dice could show the same number - In that case ans is
6*[ 5C4*5/(6^5) + 5C5*1/(6^5)] = 13/648 ~ 1/50
GMAT Club Legend
Joined: 15 Dec 2003
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Oxon, you are right, I forgot to consider that there are 6 possible values (1,2,3,4,5,6) that could be same and also when all 5 are same!
Hence, it should be:
[(1/6)^4 * 5/6 * 5C4 + (1/6)^5] * 6 = 26/6^4 = 13/648
You are absolutely right
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Paul

Manager
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That was a tough one!
Manager
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sorry!

OA would do it!
Director
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Extremely good posts (except mine). Well solved.
Senior Manager
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Oxorn is RIGHT. Thats the perfect answer.
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