jacky Posted May 9, 2019 Report Share Posted May 9, 2019 If the side of a triangle is dicided by throwing a dice 3 times. Then finding probability of forming Isoceles Triangle, is Quote Link to comment Share on other sites More sharing options...
0 Thalia Posted May 9, 2019 Report Share Posted May 9, 2019 Excluding equilateral triangles 2/9 Quote Link to comment Share on other sites More sharing options...
0 jjs323 Posted May 9, 2019 Report Share Posted May 9, 2019 3 in 20 Quote Link to comment Share on other sites More sharing options...
0 plasmid Posted May 9, 2019 Report Share Posted May 9, 2019 This sounds like it might be a homework problem, so I won’t flat out answer it but will give a hint on how to approach it. Spoiler It becomes a lot easier if you solve for the probability that you roll the dice three times and NOT get an isosceles triangle. In other words: what's the probability that you roll three times, and on each throw you roll a number that hasn't appeared yet? Quote Link to comment Share on other sites More sharing options...
0 rocdocmac Posted May 10, 2019 Report Share Posted May 10, 2019 (edited) In a nutshell ... Spoiler There are 216 possible outcomes with three dice forming ... Equilateral triangles: 6/216 (1/36) No isosceles triangles: 120/216 (5/9) Acute isosceles triangles: 45/216 (5/24) Obtuse isosceles triangles: 45/216 (5/24) All isosceles triangles (including equilateral triangles): 96/216 (4/9) Edited May 10, 2019 by rocdocmac typo Quote Link to comment Share on other sites More sharing options...
0 BobbyGo Posted May 10, 2019 Report Share Posted May 10, 2019 (edited) A couple of questions: Is a side of the triangle determined by a single die roll? Or do you sum up three rolls per side? Are non-possible triangles considered valid solutions? e.g. A roll of 1,1,6 might appear isosceles, but would not be a valid triangle. Edited May 10, 2019 by BobbyGo Quote Link to comment Share on other sites More sharing options...
0 Thalia Posted May 11, 2019 Report Share Posted May 11, 2019 (edited) On 5/8/2019 at 10:57 PM, Thalia said: Excluding equilateral triangles Hide contents 2/9 Revised answer: 7/24 without equilateral 3/8 with equilateral Both excluding impossible triangles. Edited May 11, 2019 by Thalia Quote Link to comment Share on other sites More sharing options...
0 plasmid Posted May 12, 2019 Report Share Posted May 12, 2019 This gets tricky with rolls like (1, 1, 6) that look isosceles but don't actually form triangles. How would you handle such rolls? Would you omit rolls that don't form a triangle from analysis (equivalent to saying that if you get a roll that doesn't form a valid triangle then roll again), or count them as a failure to form an isosceles triangle? And would you consider a "straight line" throw like (3, 3, 6) to be a valid triangle albeit with zero area or nah? Quote Link to comment Share on other sites More sharing options...
0 rocdocmac Posted May 13, 2019 Report Share Posted May 13, 2019 (edited) Revised ... Spoiler I was way out with my first attempt! Equilateral (EL) = 2/72 = (1/36) Acute isosceles (AI) = 16/72 (2/9) Obtuse isosceles (OI) = 5/72 Impossible triangles = 9/72 (1/8) Normal triangles = 40/72 (5/9) Total isosceles (AI+OI) = 18/72 (1/4) Including equilateral (AI+OI+EL) = 23/72 Edited May 13, 2019 by rocdocmac typo Quote Link to comment Share on other sites More sharing options...
0 rocdocmac Posted May 13, 2019 Report Share Posted May 13, 2019 (edited) Please ignore previous submission ... Spoiler Here's a visual representation including and excluding "impossible" triangles You can make your own subtotals! nal answer ... Edited May 13, 2019 by rocdocmac Quote Link to comment Share on other sites More sharing options...
0 Thalia Posted May 14, 2019 Report Share Posted May 14, 2019 On 5/11/2019 at 4:26 PM, Thalia said: Revised answer: Hide contents 7/24 without equilateral 3/8 with equilateral Both excluding impossible triangles. Well, I seem to have done some weird math when adding equilateral. New result including equilateral: 23/72 I think rocdocmac and I agree on the figure including equilateral now but we seem to have diverged on the other figure... Quote Link to comment Share on other sites More sharing options...
0 rocdocmac Posted May 14, 2019 Report Share Posted May 14, 2019 My revised answers sent in previously were not all correct. These should be fine ... Spoiler With impossible triangles/straight-line cases: Equilateral (EL) = 2/72 (1/36) Acute isosceles (AI) = 15/72 (5/24) Obtuse isosceles (OI) = 6/72 (1/12) Impossible triangles (including "straight line" cases) = 9/72 (1/8) Normal non-isosceles triangles = 40/72 (5/9) Total isosceles (AI+OI) = 21/72 (7/24) Including equilateral (AI+OI+EL) = 23/72 Without impossible triangles/straight-line cases: Equilateral (EL) = 2/63 Acute isosceles (AI) = 15/63 (5/21) Obtuse isosceles (OI) = 6/63 (2/21) Normal non-isosceles triangles = 40/63 Total isosceles (AI+OI) = 21/63 (1/3) Including equilateral (AI+OI+EL) = 23/63 Quote Link to comment Share on other sites More sharing options...
0 rocdocmac Posted May 17, 2019 Report Share Posted May 17, 2019 (edited) Excluding straight lines, impossible triangles and non-isosceles triangles, the distribution of all isosceles triangles is as follows ... Spoiler Edited May 17, 2019 by rocdocmac typo Quote Link to comment Share on other sites More sharing options...
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jacky
If the side of a triangle is dicided by throwing a dice 3 times. Then finding probability of forming Isoceles Triangle, is
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