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Bingo Odds
          # of Calls Bingo Cover All Four corners X
          1 0.00000000 0.00000000 0.00000000 0.00000000
          2 0.00000000 0.00000000 0.00000000 0.00000000
          3 0.00000000 0.00000000 0.00000000 0.00000000
          4 0.00000329 0.00000000 0.00000082 0.00000000
          5 0.00001692 0.00000000 0.00000411 0.00000000
          6 0.00005215 0.00000000 0.00001234 0.00000000
          7 0.00012492 0.00000000 0.00002880 0.00000000
          8 0.00025632 0.00000000 0.00005759 0.00000000
          9 0.00047305 0.00000000 0.00010367 0.00000000
          10 0.00080783 0.00000000 0.00017278 0.00000000
          11 0.00129986 0.00000000 0.00027150 0.00000001
          12 0.00199521 0.00000000 0.00040726 0.00000003
          13 0.00294715 0.00000000 0.00058826 0.00000008
          14 0.00421648 0.00000000 0.00082356 0.00000018
          15 0.00587167 0.00000000 0.00112304 0.00000038
          16 0.00798905 0.00000000 0.00149739 0.00000076
          17 0.01065272 0.00000000 0.00195812 0.00000144
          18 0.01395440 0.00000000 0.00251759 0.00000259
          19 0.01799309 0.00000000 0.00318894 0.00000448
          20 0.02287445 0.00000000 0.00398618 0.00000747
          21 0.02871003 0.00000000 0.00492410 0.00001206
          22 0.03561614 0.00000000 0.00601835 0.00001895
          23 0.04371249 0.00000000 0.00728537 0.00002906
          24 0.05312045 0.00000000 0.00874244 0.00004359
          25 0.06396106 0.00000000 0.01040767 0.00006411
          26 0.07635261 0.00000000 0.01229997 0.00009260
          27 0.09040799 0.00000000 0.01443910 0.00013159
          28 0.10623163 0.00000000 0.01684561 0.00018423
          29 0.12391628 0.00000000 0.01954091 0.00025441
          30 0.14353947 0.00000000 0.02254720 0.00034692
          31 0.16515993 0.00000000 0.02588753 0.00046759
          32 0.18881391 0.00000000 0.02958575 0.00062345
          33 0.21451154 0.00000000 0.03366654 0.00082296
          34 0.24223348 0.00000000 0.03815542 0.00107617
          35 0.27192783 0.00000000 0.04307870 0.00139504
          36 0.30350759 0.00000000 0.04846353 0.00179362
          37 0.33684876 0.00000000 0.05433790 0.00228842
          38 0.37178933 0.00000000 0.06073059 0.00289866
          39 0.40812916 0.00000000 0.06767123 0.00364670
          40 0.44563111 0.00000000 0.07519026 0.00455838
          41 0.48402328 0.00000001 0.08331894 0.00566344
          42 0.52300269 0.00000001 0.09208935 0.00699602
          43 0.56224021 0.00000003 0.10153441 0.00859511
          44 0.60138685 0.00000007 0.11168785 0.01050513
          45 0.64008123 0.00000015 0.12258423 0.01277651
          46 0.67795818 0.00000031 0.13425892 0.01546630
          47 0.71465810 0.00000063 0.14674812 0.01863888
          48 0.74983686 0.00000125 0.16008886 0.02236665
          49 0.78317588 0.00000245 0.17431898 0.02673088
          50 0.81439191 0.00000472 0.18947715 0.03182247
          51 0.84324614 0.00000891 0.20560286 0.03774293
          52 0.86955207 0.00001654 0.22273644 0.04460528
          53 0.89318170 0.00003023 0.24091900 0.05253511
          54 0.91406974 0.00005441 0.26019252 0.06167165
          55 0.93221528 0.00009654 0.28059978 0.07216896
          56 0.94768080 0.00016894 0.30218438 0.08419712
          57 0.96058846 0.00029180 0.32499074 0.09794358
          58 0.97111353 0.00049778 0.34906413 0.11361456
          59 0.97947539 0.00083912 0.37445061 0.13143645
          60 0.98592639 0.00139853 0.40119709 0.15165744
          61 0.99073928 0.00230569 0.42935127 0.17454913
          62 0.99419379 0.00376192 0.45896170 0.20040826
          63 0.99656346 0.00607694 0.49007775 0.22955855
          64 0.99810354 0.00972311 0.52274960 0.26235263
          65 0.99904080 0.01541468 0.55702826 0.29917406
          66 0.99956626 0.02422308 0.59296557 0.34043944
          67 0.99983122 0.03774293 0.63061418 0.38660072
          68 0.99994699 0.05832999 0.67002756 0.43814749
          69 0.99998812 0.08943931 0.71126003 0.49560945
          70 0.99999861 0.13610330 0.75436670 0.55955906
          71 1.00000000 0.20560286 0.79940351 0.63061418
          72 1.00000000 0.30840429 0.84642725 0.70944095
          73 1.00000000 0.45945946 0.89549550 0.79675676
          74 1.00000000 0.68000000 0.94666667 0.89333333
          75 1.00000000 1.00000000 1.00000000 1.00000000


My method of analysis was entirely mathematical. The probability of x marks on the card given y calls is easily calculated as combin(24,x)*combin(51,y-x)/combin(75,y). The probability that x marks will form a bingo (five in a row) is more compicated and necessitated a computer program to run through all possible combinations and tabulate the results.