iteration = 1: there are always t, 8 ways of selecting one object so each has probability 0.125 and the prob. of a score of 1 is 1 (!!) iteration = 2 results: Score frequencies: score n proportion ------ ------------ ------------ 1 56 0.875000000 2 8 0.125000000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 2 8 0.125000000 1 64 1.000000000 O.K. total = 64 = expected total = 64 iteration = 3 results: Score frequencies: score n proportion ------ ------------ ------------ 1 336 0.656250000 2 168 0.328125000 3 8 0.015625000 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 3 8 0.015625000 2 176 0.343750000 1 512 1.000000000 O.K. total = 512 = expected total = 512 iteration = 4 results: Score frequencies: score n proportion ------ ------------ ------------ 1 1680 0.410156250 2 2184 0.533203125 3 224 0.054687500 4 8 0.001953125 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 4 8 0.001953125 3 232 0.056640625 2 2416 0.589843750 1 4096 1.000000000 O.K. total = 4096 = expected total = 4096 iteration = 5 results: Score frequencies: score n proportion ------ ------------ ------------ 1 6720 0.205078125 2 21840 0.666503906 3 3920 0.119628906 4 280 0.008544922 5 8 0.000244141 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 5 8 0.000244141 4 288 0.008789062 3 4208 0.128417969 2 26048 0.794921875 1 32768 1.000000000 O.K. total = 32768 = expected total = 32768 iteration = 6 results: Score frequencies: score n proportion ------ ------------ ------------ 1 20160 0.076904297 2 181440 0.692138672 3 54320 0.207214355 4 5880 0.022430420 5 336 0.001281738 6 8 0.000030518 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 6 8 0.000030518 5 344 0.001312256 4 6224 0.023742676 3 60544 0.230957031 2 241984 0.923095703 1 262144 1.000000000 O.K. total = 262144 = expected total = 262144 iteration = 7 results: Score frequencies: score n proportion ------ ------------ ------------ 1 40320 0.019226074 2 1305360 0.622444153 3 646800 0.308418274 4 96040 0.045795441 5 8232 0.003925323 6 392 0.000186920 7 8 0.000003815 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 7 8 0.000003815 6 400 0.000190735 5 8632 0.004116058 4 104672 0.049911499 3 751472 0.358329773 2 2056832 0.980773926 1 2097152 1.000000000 O.K. total = 2097152 = expected total = 2097152 iteration = 8 results: Score frequencies: score n proportion ------ ------------ ------------ 1 40320 0.002403259 2 8361360 0.498375893 3 6867840 0.409355164 4 1342600 0.080025196 5 153664 0.009159088 6 10976 0.000654221 7 448 0.000026703 8 8 0.000000477 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 8 8 0.000000477 7 456 0.000027180 6 11432 0.000681400 5 165096 0.009840488 4 1507696 0.089865685 3 8375536 0.499220848 2 16736896 0.997596741 1 16777216 1.000000000 O.K. total = 16777216 = expected total = 16777216 iteration = 9 results: Score frequencies: score n proportion ------ ------------ ------------ 2 48444480 0.360939503 3 66279360 0.493819714 4 16828560 0.125382543 5 2420208 0.018031955 6 230496 0.001717329 7 14112 0.000105143 8 504 0.000003755 9 8 0.000000060 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 9 8 0.000000060 8 512 0.000003815 7 14624 0.000108957 6 245120 0.001826286 5 2665328 0.019858241 4 19493888 0.145240784 3 85773248 0.639060497 2 134217728 1.000000000 1 134217728 1.000000000 O.K. total = 134217728 = expected total = 134217728 iteration = 10 results: Score frequencies: score n proportion ------ ------------ ------------ 10 8 0.000000007 2 254016000 0.236570835 3 587428800 0.547085702 4 194040000 0.180713832 5 33875856 0.031549349 6 4033680 0.003756657 7 329280 0.000306666 8 17640 0.000016429 9 560 0.000000522 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 10 8 0.000000007 9 568 0.000000529 8 18208 0.000016958 7 347488 0.000323623 6 4381168 0.004080281 5 38257024 0.035629630 4 232297024 0.216343462 3 819725824 0.763429165 2 1073741824 1.000000000 1 1073741824 1.000000000 O.K. total = 1073741824 = expected total = 1073741824 iteration = 11 results: Score frequencies: score n proportion ------ ------------ ------------ 10 616 0.000000072 11 8 0.000000001 2 1187524800 0.138246082 3 4809604800 0.559911691 4 2089533600 0.243253727 5 434339136 0.050563730 6 62118672 0.007231565 7 6338640 0.000737915 8 452760 0.000052708 9 21560 0.000002510 ... and for scoring at or above cutting score cut score n proportion ------ ------------ ------------ 11 8 0.000000001 10 624 0.000000073 9 22184 0.000002583 8 474944 0.000055291 7 6813584 0.000793206 6 68932256 0.008024771 5 503271392 0.058588501 4 2592804992 0.301842228 3 7402409792 0.861753918 2 8589934592 1.000000000 1 8589934592 1.000000000 O.K. total = 8589934592 = expected total = 8589934592