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# PS: Probability

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Retired Moderator
Joined: 18 Jul 2008
Posts: 960

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28 Nov 2008, 15:23
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Mary and Joe are to throw three dice each. The score is the sum of points on all three dice. If Mary scores 10 in her attempt what is the probability that Joe will outscore Mary in his?

1) 24/64

2) 32/64

3) 36/64

4) 40/64

5) 42/64

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Manager
Joined: 27 May 2008
Posts: 200

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28 Nov 2008, 21:53
1
KUDOS

Approach,

1 - (sum <=10)

P = F.E/T.E

T.E = 6*6*6

for sum <=10

1,1,1 .... 1,1,6 ----6
1,2,1 ..... 1,2,6 ---- 6
1,3,1 ...... 1,3,6 ----6
1,4,1 ...... 1,4,5 ---- 5
1,5,1 ----- 1,5,4 ----- 4
----- 3

so 30
similarly, 26, 21,15,10,6

so 108/216 == 1/2

i will give the combination version of this shorlty..

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Manager
Joined: 18 Nov 2008
Posts: 115

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29 Nov 2008, 04:35
I think in GMAT we should always try to find the shortest way to solve a problem. In this situation could be the following:

All possible sums for throwing dice three times range from 3 to 18, so, there are 16 possible outcomes from 3 to 18. Mary scores 10 - the 8th number in this range, therefore the probability that Joe outscores Mary is (remaining 8 numbers / 16) = 1/2, or 32/64 as it is given in the answer choces.

C

Kudos [?]: 34 [0], given: 0

Re: PS: Probability   [#permalink] 29 Nov 2008, 04:35
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