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kevincan
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A scalene triangle is a triangle whose three sides are of Updated on: 30 Jul 2006, 23:47
Originally posted by kevincan on 30 Jul 2006, 02:10.
Last edited by kevincan on 30 Jul 2006, 23:47, edited 1 time in total.
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A scalene triangle is a triangle whose three sides are of different lengths. If each of three integers u,v and w is chosen at random from the 6-element set {2,4,6,8,10,12} , the probability that line segments whose lengths are u,v and,w centimeters could be used to construct a scalene triangle is between

(A) 0 and 0.03 (B) 0.03 and 0.06 (C) 0.06 and 0.09 (D) 0.09 and 0.12 (E) 0.12 and 1



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A scalene triangle is a triangle whose three sides are of 30 Jul 2006, 08:58
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3 lines that can form scalene triangle can be chosen in 6C3 or 20 ways.
Triplets-2,4,6 ; 4,6,10; 4,8,12; 2,8,10; 2,6,8, 10,12,2- do not satisfy the condition for sides of triangle. The requied prob is 14/20 or 70%
i am wrong cause do not see this opt in the ans choices :shock:
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A scalene triangle is a triangle whose three sides are of Updated on: 30 Jul 2006, 23:35
Originally posted by freetheking on 30 Jul 2006, 20:33.
Last edited by freetheking on 30 Jul 2006, 23:35, edited 1 time in total.
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kevincan
A scalene triangle is a triangle whose three sides are of different lengths. If each of three integers u,v and w is chosen at random from the 6-element set {2,4,6,8,10,12} , the probability that line segments whose lengths are u,v and,w centimeters could be used to construct a scalene triangle is between

(A) 0.75 and 0.77 (B) 0.77 and 0.79 (C) 0.79 and 0.81 (D) 0.81 and 0.83 (E) 0.83 and 0.85
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Total 6C3 = 20
Ways to form a triangle is 7, since any side of a triangle is less than a sum of two other sides
4-6-8,4-8-10,4-10-12,6-8-10,6-8-12,6-10-12,8-10-12

7/20 = 0.35...... :???
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A scalene triangle is a triangle whose three sides are of 30 Jul 2006, 21:01
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Only seven triangles are possible.

Prob = 7/20 = 0.35
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A scalene triangle is a triangle whose three sides are of 30 Jul 2006, 23:49
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corrected! Note that the choice of v is independent of the choice of u. That is to say that u could be the same integer as v and/or w!
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A scalene triangle is a triangle whose three sides are of 31 Jul 2006, 02:03
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kevincan
corrected! Note that the choice of v is independent of the choice of u. That is to say that u could be the same integer as v and/or w!
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if only 7 triangles ar epossible (I just trust on that)

than this addition doesn't make difference...

total varians 6P3 = 6!/3!= 120

Possible= 7*3!=42

42/120= 0.35 thus (E) Pobability 0.12-1

GL!
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A scalene triangle is a triangle whose three sides are of 01 Aug 2006, 07:40
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If selection of any side is independent of previous selection, then we could select 3 sides in 6*6*6=216 ways.

as explained in other posts only 7 possible ways to form triangle

prob=7/216 = .03
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A scalene triangle is a triangle whose three sides are of 01 Aug 2006, 08:38
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...and for each of these 7, there are 6 ways to write the combination, each of which you have counted in 6^3.

so (6*7)/(6*6*6) or about 7/36.

7/36 > (6/36 = 1/6) and 1/6 is already in [0.12,1), so

E

assuming we're choosing each element with replacement.
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A scalene triangle is a triangle whose three sides are of 05 Aug 2006, 20:52
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Interesting question...
I misinterpreted the question thinking that we can pick the same digit multiple times.

20 different combinations of 3 digits with 7 options adding to a Scalene triangle. therefore, prob. = 7/20 = .35



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