------ art_5624_31398283.1191160961804 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 7bit Content-Disposition: inline 2007/9/28, Ruby Quiz <james / grayproductions.net>: > > You just did some probability calculations, and don't know if the answers > are > correct. So you write a program to verify the results. If you have eight > dice, > and throw them all at once, what is the probability that there are AT > LEAST > three fives? Try to write a program that find out the "number of > desirable > outcomes" / "number of possible outcomes" by iterating through all the > possible > outcomes of the dice throw. Hi, My solution can be found at http://pastie.caboo.se/102192 #At least 3 fives from 8 dice: $ time ./rq141_probableiterations_rafc.rb 8 3 Number of desirable outcomes is 226491 Number of possible outcomes is 1679616 Probability is 0.134846893575674 real 0m20.526s user 0m18.449s sys 0m2.060s #It can do non-cubic dice: at least 2 fives from a d10, 2 d6's and one d20: $ ./rq141_probableiterations_rafc.rb -d,2d6,d20 -s 2 1 [1, 1, 1, 1] 889 [2, 2, 3, 9] 1777 [3, 3, 5, 17] 2665 [4, 5, 2, 5] < 3553 [5, 6, 4, 13] 4441 [7, 2, 1, 1] 5329 [8, 3, 3, 9] 6217 [9, 4, 5, 17] 7105 [10, 6, 2, 5] Number of desirable outcomes is 515 Number of possible outcomes is 7200 Probability is 0.0715277777777778 #Full show-off mode if launched without parameters: $ ./rq141_probableiterations_rafc.rb 5 usual dice; # of sixes greater than # of ones: 1 [1, 1, 1, 1, 1] 501 [1, 3, 2, 6, 3] 1001 [1, 5, 4, 5, 5] 1501 [2, 1, 6, 5, 1] 2001 [2, 4, 2, 4, 3] 2501 [2, 6, 4, 3, 5] < 3001 [3, 2, 6, 3, 1] 3501 [3, 5, 2, 2, 3] 4001 [4, 1, 4, 1, 5] 4501 [4, 3, 6, 1, 1] 5001 [4, 6, 1, 6, 3] < 5501 [5, 2, 3, 5, 5] 6001 [5, 4, 5, 5, 1] 6501 [6, 1, 1, 4, 3] 7001 [6, 3, 3, 3, 5] < 7501 [6, 5, 5, 3, 1] Number of desirable outcomes is 2676 Number of possible outcomes is 7776 Probability is 0.344135802469136 3 tetrahedra (d4); sum of evens smaller than sum of odds: 1 [1, 1, 1] < 2 [1, 1, 2] 3 [1, 1, 3] < 4 [1, 1, 4] 5 [1, 2, 1] 6 [1, 2, 2] 7 [1, 2, 3] < 8 [1, 2, 4] 9 [1, 3, 1] < 10 [1, 3, 2] < 11 [1, 3, 3] < 12 [1, 3, 4] 13 [1, 4, 1] 14 [1, 4, 2] 15 [1, 4, 3] 16 [1, 4, 4] 17 [2, 1, 1] 18 [2, 1, 2] 19 [2, 1, 3] < 20 [2, 1, 4] 21 [2, 2, 1] 22 [2, 2, 2] 23 [2, 2, 3] 24 [2, 2, 4] 25 [2, 3, 1] < 26 [2, 3, 2] 27 [2, 3, 3] < 28 [2, 3, 4] 29 [2, 4, 1] 30 [2, 4, 2] 31 [2, 4, 3] 32 [2, 4, 4] 33 [3, 1, 1] < 34 [3, 1, 2] < 35 [3, 1, 3] < 36 [3, 1, 4] 37 [3, 2, 1] < 38 [3, 2, 2] 39 [3, 2, 3] < 40 [3, 2, 4] 41 [3, 3, 1] < 42 [3, 3, 2] < 43 [3, 3, 3] < 44 [3, 3, 4] < 45 [3, 4, 1] 46 [3, 4, 2] 47 [3, 4, 3] < 48 [3, 4, 4] 49 [4, 1, 1] 50 [4, 1, 2] 51 [4, 1, 3] 52 [4, 1, 4] 53 [4, 2, 1] 54 [4, 2, 2] 55 [4, 2, 3] 56 [4, 2, 4] 57 [4, 3, 1] 58 [4, 3, 2] 59 [4, 3, 3] < 60 [4, 3, 4] 61 [4, 4, 1] 62 [4, 4, 2] 63 [4, 4, 3] 64 [4, 4, 4] Number of desirable outcomes is 20 Number of possible outcomes is 64 Probability is 0.3125 3 usual dice and 2 dodecahedra (d12): product greater than 1000 1 [1, 1, 1, 1, 1] 2501 [1, 3, 6, 5, 5] 5001 [1, 6, 5, 9, 9] < 7501 [2, 3, 5, 2, 1] 10001 [2, 6, 4, 6, 5] < 12501 [3, 3, 3, 10, 9] < 15001 [3, 6, 3, 3, 1] 17501 [4, 3, 2, 7, 5] 20001 [4, 6, 1, 11, 9] < 22501 [5, 3, 1, 4, 1] 25001 [5, 5, 6, 8, 5] < 27501 [6, 2, 5, 12, 9] < 30001 [6, 5, 5, 5, 1] Number of desirable outcomes is 13926 Number of possible outcomes is 31104 Probability is 0.447723765432099 Regards, Raf ------ art_5624_31398283.1191160961804--