Statistics

Problem Statement for "TournamentWinner"

Problem Statement

You are running a local tournament with 8 competitors. The tournament will consist of 3 rounds and will be organized as follows.
In round 1 game i is played between competitors 2*i and 2*i+1 (0<=i<=3). 4 winning competitors advance to round 2.
In round 2 game i is played between the winners of games 2*i and 2*i+1 (0<=i<=1). 2 winning competitors advance to round 3.
Finally, the winners of round 2 games play one game in round 3 to determine the winner of the tournament.
You are given a int[] P describing the percent probabilities of each competitor winning a game against another competitor. The first 7 elements of P are the probabilities of competitor 0 winning a game against competitors 1 through 7, the next 6 elements are the probabilities of competitor 1 winning a game against competitors 2 through 7, etc.
Return a double[] containing exactly 8 elements, where the i-th element is the probability of competitor i winning the tournament.

Definition

Class:
TournamentWinner
Method:
winningProbabilities
Parameters:
int[]
Returns:
double[]
Method signature:
double[] winningProbabilities(int[] P)
(be sure your method is public)

Notes

  • The games played in the tournament will not end in a tie.
  • Each element of your return must have an absolute or relative error less than 1e-9.

Constraints

  • P will contain exactly 28 elements.
  • Each element of P will be between 0 and 100, inclusive.

Examples

  1. {5, 0, 10, 15, 20, 25, 30, 0, 35, 40, 45, 50, 55, 100, 100, 100, 100, 100, 60, 65, 70, 75, 80, 85, 90, 95, 50, 50}

    Returns: {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

    Competitor 2 wins a game against any other competitor with probability 1.0, so he will win the tournament, leaving no chances to other competitors.

  2. {100, 25, 0, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 0, 25, 25, 25, 25, 50, 25, 25, 25, 100, 25, 100, 25, 25, 0}

    Returns: {0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0 }

    In round 1, players 0, 3, 4 and 7 win against players 1, 2, 5 and 6, respectively. In round 2, 3 wins against 0 and 4 wins against 7. Finally, both 3 and 4 have a 50% chance to win against the opponent in round 3 and to win the tourney.

  3. {50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50}

    Returns: {0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125, 0.125 }

    All competitors have equal chances.

  4. {100,100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100, 100}

    Returns: {1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

  5. { 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}

    Returns: {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0 }

  6. {100, 50, 50, 50, 50, 50, 50, 0, 50, 50, 50, 50, 50, 100, 50, 50, 50, 50, 0, 50, 50, 50, 100, 50, 50, 0, 50, 100}

    Returns: {0.25, 0.0, 0.25, 0.0, 0.25, 0.0, 0.25, 0.0 }

    Competitors 0, 2, 4 and 6 win their games in round 1 and have equal chances in later rounds.

  7. { 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 100, 100, 100, 10, 20, 30}

    Returns: {0.125, 0.125, 0.125, 0.125, 0.5, 0.0, 0.0, 0.0 }

    Competitor 4 will get to round 3 for sure, while competitors 0, 1, 2 and 3 have equal chances to get to round 3.

  8. { 10, 20, 40, 70, 90, 40, 20, 30, 50, 80, 80, 30, 30, 60, 90, 70, 20, 40, 100, 60, 10, 50, 50, 0, 60, 10, 70, 80}

    Returns: {0.012852000000000002, 0.13167, 0.132486, 0.048348, 0.007163999999999997, 0.030865999999999998, 0.593256, 0.043358 }

  9. { 1, 2, 4, 7, 11, 16, 22, 3, 5, 8, 12, 17, 23, 6, 9, 13, 18, 24, 10, 14, 19, 25, 15, 20, 26, 21, 27, 28}

    Returns: {6.88919608E-5, 0.009061234459199999, 0.011498979459599998, 0.1853675541204, 0.0328889066112, 0.18542493028680002, 0.17985791390280004, 0.3958315891991999 }

  10. { 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 3, 4, 5, 6, 7, 4, 5, 6, 7, 5, 6, 7, 6, 7, 7}

    Returns: {2.0172640949999997E-5, 0.0019970914540499997, 0.00199688769, 0.063907198215, 0.0033263999999999998, 0.06254324999999998, 0.06185199999999999, 0.8043569999999999 }

  11. {58,40,7,17,38,8,53,83,47,6,15,65,79,98,23,79,55,2,53,63,98,79,7,75,7,66,59,88}

    Returns: {0.06619564518224, 0.11296900174559998, 0.26801020600704, 0.011226876403200008, 0.03920208563712, 0.31945115546927993, 0.15156468302624, 0.03138034652928 }

  12. {37,19,4,74,5,41,39,72,84,96,8,47,16,64,42,83,43,34,28,73,58,76,76,27,99,33,79,99}

    Returns: {0.0226742282304, 0.26047289403072, 0.14015246844672, 0.08683216934399997, 0.06894017044992003, 0.04708043639040001, 0.37345608457344, 3.915485344000003E-4 }

  13. {58,11,1,18,73,18,93,8,75,42,92,45,83,41,52,53,1,78,67,89,55,96,12,96,65,27,48,96}

    Returns: {0.009753519887999999, 0.11365283102880004, 0.07800126805824001, 0.26253140312448003, 0.0511602341472, 0.059280170357759995, 0.42295369540608, 0.0026668779894400024 }

  14. {33,53,45,29,94,18,87,12,61,71,98,12,38,64,87,2,3,71,18,32,70,9,93,37,23,73,21,62}

    Returns: {0.0732693363864, 0.07985083674047999, 0.22707570651392, 0.05640224228928, 0.10833185417472, 0.021964596438399986, 0.3076731776563201, 0.12543224980048004 }

  15. {27,83,71,84,97,40,52,49,2,75,31,32,61,97,11,14,1,5,31,49,87,80,9,32,55,45,0,64}

    Returns: {0.13530439079424, 0.15014922202231998, 0.0249001783512, 0.017290497658680015, 0.01812650317776, 0.1591902014976, 0.27853362109760005, 0.21650538540059996 }

  16. {16,12,35,87,52,14,40,16,30,84,79,60,32,18,61,53,6,87,60,19,96,0,98,57,75,65,98,94}

    Returns: {0.02786895202304, 0.16966767859776, 0.05961133988352, 0.414596517872, 0.18768573745152, 0.008083240707840009, 0.12109255570944003, 0.01139397775488001 }

  17. {38,17,34,39,61,93,38,61,6,89,21,70,22,1,11,38,2,93,100,75,17,89,28,75,1,90,30,37}

    Returns: {0.06378011822136, 0.011967835224799998, 0.0034006814206400003, 0.6670564677849599, 0.00698044515168, 0.10974099542399998, 0.03738806610839999, 0.09968539066415999 }

  18. {26,7,33,57,28,97,59,49,100,88,93,36,13,50,22,32,87,68,36,77,51,94,13,22,0,63,26,22}

    Returns: {0.02772569592000001, 0.21707568709400005, 0.182005524144, 0.07367034714000001, 0.002427126416, 0.091063342656, 0.040725769194, 0.36530650743600007 }

  19. {9,34,86,99,100,45,16,10,11,0,9,13,75,44,20,53,46,34,62,73,40,83,20,85,13,34,51,1}

    Returns: {0.029879360568000002, 0.043971415488000015, 0.16004397404160003, 0.35980883652000006, 0.015939590867200006, 0.1599975828672, 0.0033475299408000005, 0.2270117097072 }

  20. {35,42,33,28,61,46,59,27,13,15,94,1,11,25,4,24,89,68,93,83,56,83,99,29,2,48,91,48}

    Returns: {0.06169281005999999, 0.009413894490000001, 0.1106855598, 0.45182438399999997, 0.05695968761999999, 0.0020072036950000024, 0.15479561669999997, 0.152620843635 }

  21. {59,65,86,100,46,59,53,84,18,27,44,25,100,41,15,81,46,3,62,52,45,30,14,56,32,48,18,78}

    Returns: {0.25672975674279996, 0.08334515762496, 0.054317230224480005, 0.11380587056832005, 0.022977222381120006, 0.17439659872200003, 0.20712707196480007, 0.08730109177151998 }

  22. {6,81,51,12,38,57,94,73,74,28,93,93,41,61,19,73,80,1,67,45,99,74,82,48,20,78,95,53}

    Returns: {0.021940739805599997, 0.40134803390880003, 0.05952903527376002, 0.07868339092692, 0.1998579828024, 0.027315735430320003, 0.024597291435199994, 0.186727790417 }

  23. {32,43,35,16,88,23,69,26,83,45,42,12,15,54,63,19,53,21,32,44,60,75,23,95,91,97,32,79}

    Returns: {0.08613739541887999, 0.13757662941288, 0.10990822857696, 0.06755371232375999, 0.11677344827455997, 0.38783374057120007, 0.017573483437760017, 0.07664336198399997 }

  24. {35,56,76,98,61,60,29,14,40,18,99,98,2,29,58,68,72,37,52,62,73,74,40,15,80,84,66,32}

    Returns: {0.15587758368, 0.12859215969600002, 0.12448248747200001, 0.21364959206399997, 0.10094982912, 0.12571684632, 0.035055962624000014, 0.11567553902399996 }

  25. {78,23,98,45,23,81,64,30,4,37,50,79,74,81,45,24,1,70,36,83,12,66,55,34,54,20,28,54}

    Returns: {0.17942560779, 0.0356171795672, 0.19693249412759994, 0.01706479397279999, 0.13264942838400004, 0.07705853366399998, 0.2771267219064, 0.08412524058799997 }

  26. {4,34,22,51,100,56,97,30,24,37,39,38,74,98,18,82,42,37,47,7,96,95,53,79,56,54,23,97}

    Returns: {0.00886289585536, 0.11037077459711998, 0.2869608669681599, 0.008132321905440006, 0.31403395188656, 0.07790314189968, 0.18468567277599995, 0.009050374111680007 }

  27. {75,13,9,97,46,18,11,17,30,74,51,86,90,56,1,99,14,51,23,24,28,74,47,8,61,94,88,37}

    Returns: {0.038498061618000005, 0.03836952577600001, 0.27870394272000004, 0.12175407990899997, 0.15263098086599997, 0.174491380388, 0.13103284414, 0.06451918458300002 }

  28. {21,75,77,56,51,23,5,17,32,84,43,85,22,6,64,31,75,52,72,4,66,1,23,41,46,2,92,32}

    Returns: {0.06090091084224, 0.1388131989632, 0.02105844371136, 0.15536218611600003, 0.0285678902688, 0.3780353345999999, 0.10225409170496003, 0.11500794379344 }

  29. {42,79,10,29,53,70,94,35,77,75,10,2,34,37,74,56,56,62,6,37,91,53,31,39,79,91,1,39}

    Returns: {0.10246003103027998, 0.11743839685872001, 0.10719216944368001, 0.14014905401448002, 0.1066565151012, 0.16680726335760002, 0.048870100443840006, 0.2104264697502 }

  30. {82,92,48,34,8,53,95,55,45,97,15,34,84,80,43,20,96,54,66,94,14,39,9,29,67,30,51,59}

    Returns: {0.3043931037056, 0.03778013341800002, 0.0691729472928, 0.0515620456592, 0.0222964854984, 0.28420065633960007, 0.19794769578080001, 0.03264693230560001 }

  31. {67,91,13,3,36,68,2,25,77,70,38,80,91,12,45,39,40,88,35,30,19,82,72,61,37,31,95,15}

    Returns: {0.022644083800000006, 0.16673830216559998, 0.022272614841599998, 0.2976835866048, 0.17905139038080004, 0.159972810368, 0.041692732848, 0.10994447899120002 }

  32. {77,97,96,38,40,28,23,31,57,86,31,23,45,4,20,51,56,57,49,54,39,28,57,37,7,67,79,11}

    Returns: {0.22062931292864002, 0.05343744306631998, 0.0038373235747199996, 0.04796668412928001, 0.032045843688, 0.19819384853087998, 0.039166837921199994, 0.40472270616095996 }

  33. {68,65,87,82,64,64,32,84,29,3,81,29,4,100,45,32,35,93,80,97,51,28,53,1,8,48,65,9}

    Returns: {0.20205564132000003, 0.07704132441599998, 0.19929790273200004, 0.0, 0.019505344716, 0.12136642003199999, 0.037236222612, 0.34349714417199995 }

  34. {69,85,78,74,18,60,35,99,18,3,76,32,74,71,91,44,86,90,59,19,50,37,20,15,58,26,92,7}

    Returns: {0.16452899226719997, 0.15297010766820004, 0.0437016867508, 0.032414128124000005, 0.047400488062199986, 0.4637272398304001, 0.0244104279888, 0.07084692930839999 }

  35. {58,90,25,11,21,10,64,51,94,74,72,92,1,55,63,83,95,15,96,17,36,39,34,52,97,47,31,85}

    Returns: {0.060636158144999994, 0.225035447742, 0.11532983563199999, 0.08822381911199996, 0.09036302485, 0.16414635111599996, 0.20954151643499996, 0.046723846968 }

  36. {4,33,86,86,31,28,47,93,2,89,9,62,80,52,71,91,65,87,60,94,5,60,85,72,35,13,69,1}

    Returns: {0.013327260700799998, 0.35676406385279996, 0.040335409399999966, 0.28749859582079995, 0.07553361687119999, 0.049137642316800005, 0.0023783597288000004, 0.17502505130879997 }

  37. {95,9,57,7,34,88,20,22,56,47,21,93,93,92,93,75,41,78,60,28,29,67,98,55,1,64,95,99}

    Returns: {0.052957236422399974, 0.008345888284800006, 0.5781090879095999, 0.01580835330479999, 0.10244717194879993, 0.004152792526000003, 0.23533693424999996, 0.002842535353600002 }

  38. {65,64,20,29,42,2,81,68,91,31,44,84,51,36,8,67,32,82,82,14,24,84,66,28,31,20,25,16}

    Returns: {0.1348186298368, 0.14574615144319997, 0.07458930817919998, 0.24941712271359995, 0.1094376833088, 0.052815400352, 0.07502777466879999, 0.15814792949759998 }

  39. {12,91,65,13,36,30,81,12,44,99,85,19,78,44,36,5,44,6,24,92,30,56,5,53,9,81,41,26}

    Returns: {0.05102507592, 0.20669620674560002, 0.0270649080416, 0.2152501716736, 0.0054284502944000005, 0.21991711636800002, 0.036098718489599994, 0.23851935246720002 }

  40. {97,0,70,90,93,25,3,14,91,61,33,75,16,60,36,50,69,50,83,57,73,89,39,72,45,62,70,9}

    Returns: {0.156992673684, 0.004478075078400005, 0.28675115751360003, 0.08678910422160002, 0.08042067451080001, 0.15943867250559998, 0.013012510896000001, 0.21211713159000006 }

  41. {18,14,7,11,67,16,18,74,91,47,0,21,55,65,20,87,12,74,68,63,27,44,15,26,40,66,6,60}

    Returns: {0.007210221480000003, 0.17586726222, 0.1463937488, 0.04038703451999999, 0.027697725480000004, 0.25874720970000004, 0.19380055199999996, 0.1498962458 }

  42. {35,12,31,5,47,80,56,69,54,49,93,28,20,82,14,38,90,6,22,21,33,31,85,99,88,80,3,45}

    Returns: {0.00842671389, 0.20329398277500002, 0.06510463349000002, 0.022726190002500007, 0.55798383212, 0.02228839526250001, 0.007415815522500002, 0.11276043693750001 }

  43. {40,38,65,52,86,93,46,80,77,66,59,79,0,35,17,59,46,36,6,81,23,79,63,11,92,58,3,19}

    Returns: {0.127278895282, 0.21326023282200002, 0.037783438784, 0.065498847609, 0.26190139752, 0.015439690780000001, 0.043891000691999985, 0.234946496511 }

  44. {88,36,16,49,95,30,33,38,72,2,8,45,22,81,91,90,81,84,98,31,57,8,86,12,48,87,16,81}

    Returns: {0.1135984629472, 0.016942980768479998, 0.43314339423312004, 0.08179853903423996, 0.039892940069759984, 0.02225119236928, 0.24416964, 0.048202850577919974 }

  45. {95,16,79,15,65,93,17,64,59,57,46,46,40,42,15,46,67,39,63,31,68,60,10,44,32,88,64,56}

    Returns: {0.2862833986240001, 0.013866962720000011, 0.15600943411200002, 0.05185541504, 0.030043661120000006, 0.32360222188800003, 0.018860785887999998, 0.119478120608 }

  46. {8,95,46,66,27,62,68,58,73,57,16,88,27,84,91,2,84,37,10,48,56,36,44,58,96,99,99,25}

    Returns: {0.030835673984, 0.19572827775999999, 0.132438921216, 0.015727364352000003, 0.127179225536, 0.47861964057600004, 0.007910008064000001, 0.011560888512000008 }

  47. {67,100,21,11,56,79,9,40,12,41,6,85,81,93,14,53,72,97,39,85,64,29,18,99,47,13,28,5}

    Returns: {0.1404128365059, 0.07633988813880002, 0.14522009594399998, 0.025050294303999986, 0.07416936714239998, 0.10985925730050002, 0.008008978744800001, 0.4209392819196 }

  48. {53,93,78,80,56,6,19,20,54,88,20,49,10,79,46,14,45,79,15,5,90,89,45,38,93,59,77,70}

    Returns: {0.202266645135, 0.059243483973000007, 0.11708308850850002, 0.028969868928, 0.08490094420500001, 0.23328686642799998, 0.24691118979450005, 0.027337913028 }

  49. {33,94,91,21,79,51,28,73,67,18,35,90,12,26,30,69,47,50,76,50,51,51,17,27,27,87,62,33}

    Returns: {0.17922994487969998, 0.14542076042359997, 0.031273061355899995, 0.09569944764599997, 0.031992693822, 0.2747185616869999, 0.023958686399999995, 0.21770684378579996 }

  50. {91,52,4,59,42,47,52,4,37,4,62,26,13,23,68,51,57,69,37,83,42,8,71,3,86,71,49,15}

    Returns: {0.07330317452639999, 0.004562976352049998, 0.0774442724952, 0.27550430517225, 0.29834643736864996, 0.040978238517500015, 0.0648388597248, 0.16502173584315 }

  51. {56,43,69,66,86,33,23,44,29,22,84,50,94,91,100,55,79,60,76,7,83,49,87,87,52,11,17,38}

    Returns: {0.12569197093152001, 0.0921019966944, 0.43378916520576, 0.02908331823959999, 0.1381642156536, 0.006465357084159999, 0.03299243449216, 0.14171154169880001 }

  52. {26,14,2,71,25,67,26,54,74,43,59,15,97,62,0,6,60,12,31,33,23,0,99,66,19,69,59,67}

    Returns: {0.014190919624959998, 0.2329126696512, 0.05905088121599999, 0.03559643954048, 0.36683185152240005, 0.004256431790400003, 0.15164608193776, 0.1355147247168 }

  53. {58,40,85,16,89,60,16,82,23,95,98,13,42,92,58,70,15,99,56,91,19,32,44,35,61,99,44,77}

    Returns: {0.1547101834944, 0.23409871325568, 0.22885166895359998, 0.02033568509183999, 0.07334607481344, 0.074553733408, 0.16646403711168, 0.04763990387136001 }

  54. {21,90,37,15,76,69,40,95,23,55,6,100,15,66,37,68,47,45,87,92,92,59,59,28,1,40,100,29}

    Returns: {0.08545077073554, 0.1703143780528, 0.02106765417240001, 0.19654322509807998, 0.022770208752039996, 0.20078520137760003, 0.0171511472184, 0.28591741459313996 }

  55. {27,11,49,28,49,41,11,24,16,76,6,54,37,16,96,76,7,42,45,13,48,99,42,25,25,48,3,100}

    Returns: {0.048511591848, 0.054174811392, 0.045231139935999996, 0.23931513395999998, 0.048900125399999994, 0.21073926758400002, 0.35312792988, 0.0 }

  56. {62,70,19,40,36,18,2,2,6,69,2,90,99,4,32,0,66,20,6,8,40,35,62,36,63,46,72,75}

    Returns: {0.034019403472, 0.015009226320000001, 0.008925376256000001, 0.19952834179199996, 0.23214652336799996, 0.17687529552, 0.27622553279999995, 0.05727030047199999 }

  57. {84,18,93,93,46,37,75,96,42,62,22,81,80,31,24,10,52,5,34,65,34,12,43,1,19,92,38,95}

    Returns: {0.25411561056, 0.0477232848048, 0.061946392134, 0.05126374253759999, 0.0025290617356000006, 0.31572145413720004, 0.25048908881459997, 0.016211365276200013 }

  58. {25,98,13,78,72,59,1,81,14,60,14,29,78,93,7,96,35,87,97,76,11,6,45,2,83,38,25,59}

    Returns: {0.121317159425, 0.23488521332250006, 0.07126214500874997, 0.021314394543749986, 0.0647947359675, 0.10360843737750003, 0.29694393731, 0.08587397704500001 }

  59. {4,49,6,69,56,31,64,31,42,96,87,59,30,85,3,62,10,81,57,32,20,79,27,34,66,86,32,6}

    Returns: {0.010595268614400001, 0.17731399847039997, 0.3564836733479999, 0.05537744362080001, 0.10711787353919998, 0.08474117551839999, 0.012347540740799998, 0.19602302614799996 }

  60. {8,27,95,89,77,82,1,78,62,98,1,92,2,45,60,4,84,10,42,88,92,17,51,16,87,6,72,50}

    Returns: {0.03845519776, 0.4267289691200001, 0.06440587703999999, 0.13705365388000001, 0.046789101360000016, 0.14869995504000003, 0.04202338559999999, 0.09584386020000002 }

  61. {25,100,22,83,68,55,96,89,96,0,39,51,36,91,61,5,68,15,17,63,39,43,20,78,51,31,98,11}

    Returns: {0.16645209865000005, 0.23711177313, 0.012154282139999998, 0.011022504300000001, 0.08179998130500002, 0.40838240519999996, 0.030837408029999996, 0.05223954724500001 }

  62. {73,28,79,8,94,52,9,15,64,66,36,29,74,20,61,2,34,87,1,36,75,52,55,61,49,23,34,19}

    Returns: {0.12810587967200002, 0.08998522696800001, 0.093348656073, 0.07569110003999999, 0.2169198408080001, 0.05744483512200001, 0.052735381181999996, 0.285769080135 }

  63. {53,54,61,77,2,71,100,24,100,27,60,30,25,87,99,14,32,78,20,24,24,20,55,21,41,34,61,6}

    Returns: {0.19645772445930001, 0.05574788665599999, 0.33189968012399995, 0.005708582724000001, 0.045947782023000004, 0.21884154299099995, 0.025097857022699996, 0.12029894399999998 }

  64. {8,38,13,2,2,42,84,26,89,77,77,100,50,59,75,61,71,78,15,7,87,47,86,34,75,85,74,74}

    Returns: {0.005501694575999998, 0.40651768172384, 0.30960119442911993, 0.033285910640639994, 0.11471815486207998, 0.04192976792256001, 0.06400660020911998, 0.024438995636640006 }

  65. {79,35,82,19,73,46,48,7,69,43,71,38,60,57,87,43,90,15,2,83,48,37,8,18,44,62,7,76}

    Returns: {0.25310537061952004, 0.040762320318719986, 0.21264777752063999, 0.05387963355168001, 0.010344819669120002, 0.1722680261952, 0.11552518389312001, 0.14146686823200003 }

  66. {29,42,30,9,65,19,92,13,9,75,63,87,29,65,62,63,58,69,25,63,56,100,26,80,92,66,19,73}

    Returns: {0.0517479034212, 0.0537174354864, 0.320192195336, 0.17658818883650002, 0.11629549050600001, 0.1450978913544, 0.09858259447079998, 0.037778300588700006 }

  67. {23,81,59,71,17,24,71,31,27,42,31,71,92,96,73,71,70,14,53,99,15,52,63,17,55,52,1,30}

    Returns: {0.10663353713960003, 0.16664065183920002, 0.25067528879999995, 0.012427936272000012, 0.096838928424, 0.028776588413600004, 0.08339447176200002, 0.2546125973495999 }

  68. {8,78,7,74,36,97,15,56,42,66,49,49,62,83,98,55,93,78,56,3,27,27,68,43,90,59,20,64}

    Returns: {0.0365451783296, 0.28336897189888, 0.30789180162047997, 0.03655150274560001, 0.09531497601024, 0.07817526824959999, 0.11726095237120003, 0.04489134877439999 }

  69. {28,74,95,27,52,12,40,54,89,50,36,17,50,71,8,72,55,84,85,42,12,64,21,34,62,7,99,31}

    Returns: {0.08442106473248003, 0.15367233959639998, 0.17485094333879997, 0.010817792669760004, 0.07419163497312001, 0.27797038819520004, 0.19859286335039997, 0.025482973143839998 }

  70. {88,89,21,23,8,18,44,99,45,11,28,20,8,18,2,98,3,56,40,72,34,49,42,56,85,51,72,46}

    Returns: {0.05573452275072002, 0.01229442568704, 0.0076732793424, 0.32065148512672015, 0.20329839956160006, 0.17771749752768007, 0.15564848802720002, 0.06698190197664003 }

  71. {15,49,6,82,73,21,23,3,100,14,67,98,0,32,76,100,49,15,69,74,81,9,82,8,89,50,88,22}

    Returns: {0.0190386457872, 0.21090805841920002, 0.19924430869760001, 0.06396513007679999, 0.3550806954224, 0.032449789468800005, 0.037227758585600006, 0.0820856135424 }

  72. {14,23,69,48,20,84,79,35,79,97,91,28,96,58,39,46,15,54,36,17,10,2,86,96,59,78,64,1}

    Returns: {0.03429111544992001, 0.44161029116848005, 0.17634549484656004, 0.019485796915200002, 0.17397154433088002, 0.03373816030368001, 4.916290204800002E-4, 0.12006596796480001 }

  73. {62,76,68,17,22,34,55,87,34,47,58,1,73,66,18,58,73,36,62,3,20,63,50,94,65,20,1,46}

    Returns: {0.15608486112000003, 0.125409820188, 0.04884441592800001, 0.07816756495199999, 0.266875817236, 0.032510238232000006, 0.141796126448, 0.150311155896 }

  74. {66,64,65,17,62,9,38,84,16,52,29,65,52,97,28,28,63,53,21,22,85,40,62,98,72,9,22,4}

    Returns: {0.12692162958288, 0.14019282653568, 0.11267706395200001, 0.004737958051680004, 0.31730664476544, 0.046889716510080004, 0.00844234530624, 0.24283181529599998 }

  75. {28,56,76,81,7,97,51,25,91,84,83,32,33,16,85,19,47,83,83,89,77,82,79,29,25,73,34,81}

    Returns: {0.152154614976, 0.2940122606111999, 0.060082397081599986, 0.08946462460319997, 0.03707027387648, 0.05319167236991999, 0.24096891294719996, 0.07305524353439997 }

  76. {61,7,32,29,89,24,84,89,71,64,38,54,31,53,54,14,99,23,48,75,87,6,74,65,84,1,86,59}

    Returns: {0.041815454249999995, 0.17726677649616, 0.20055865267871995, 0.14820627615713997, 0.25427857951477995, 0.051031019059799995, 0.08131878913675998, 0.045524452706639996 }

  77. {23,9,32,43,17,93,9,97,81,97,79,62,81,67,48,22,1,76,30,3,67,38,50,17,6,43,47,93}

    Returns: {0.026013267651000004, 0.49081556770400003, 0.020580237775999998, 0.048602765178, 0.015729196570500002, 0.08619819218399999, 0.29826128766, 0.013799485276499988 }

  78. {98,20,75,82,30,37,48,44,4,60,86,92,51,12,74,53,39,75,90,52,45,91,46,41,24,86,69,19}

    Returns: {0.2983781071152001, 0.001205281827200001, 0.06099534333312001, 0.16886259808704002, 0.021221390731520007, 0.24413421494592, 0.0401199767712, 0.16508308718880005 }

  79. {77,9,7,62,32,18,35,27,35,91,27,65,0,63,30,34,96,74,63,14,33,63,54,24,96,30,74,53}

    Returns: {0.022982432599279998, 0.04130911392495999, 0.3254408322984, 0.12788963146496, 0.16613892700991997, 0.17021840919999998, 0.12139784289279998, 0.024622810609680003 }

  80. {83,2,29,74,18,22,69,58,20,72,37,73,7,52,100,27,100,24,69,73,35,4,53,93,37,85,45,10}

    Returns: {0.07186580603840001, 0.01980098177120001, 0.19631348522240002, 0.12150211674239998, 0.035929292582400005, 0.132254307304, 0.0036734046047999995, 0.4186606057344 }

  81. {5, 0, 10, 15, 20, 25, 30, 0, 35, 40, 45, 50, 55, 100, 100, 100, 100, 100, 60, 65, 70, 75, 80, 85, 90, 95, 50, 50 }

    Returns: {0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 }

  82. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28 }

    Returns: {1.775904416E-5, 0.01070940223584, 0.02218023527104001, 0.16609464344896002, 0.04679774831712001, 0.16728890743488, 0.16743515330976005, 0.4194761509382401 }

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