The 2nd column in the table below shows the single-board
probability that all four corners will be filled when the "Nth" number
is called. The 3rd column shows the single-board cumulative probability
that all four corners will be filled on or before the "Nth" number is
called.
The 4th and 5th columns in the table show similar data,
but for a large "X" (both diagonals filled). Note: these probabilities
are valid for any pattern that requires 8 defined location hits in
addition to the center "free" space. Examples include: A solid center,
a big "+" sign, and the letter "T".
If we look at the table below we see that when the 20th
number is called in a Bingo game we get the following probabilities.
1) A single board has a 0.000797236 probability of filling all 4
corners when the 20th number is called.
2) A single board has a 0.00398618 probability of filling all 4 corners
on or before 20 numbers are called.
3) A single board has a 2.98665E-06 probability of filling both
diagonals when the 20th number is called.
4) A single board has a 7.46663E-06 probability of filling both
diagonals on or before the 20th number is called.
Computer program and data by
Bill Butler
Quantity 4
Corners
Cumulative Letter
X Cumulative
of Bingo
Probability 4
Corners
Probability Probability
Numbers
This Turn
Probability This
Turn Letter X
Picked
1 Board 1
Board 1
Board 1 Board
-------------------------------------------------------------------------
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4 8.22741E-07
8.22741E-07
0
0
5 3.29096E-06
4.1137E-06
0
0
6 8.22741E-06
1.23411E-05
0
0
7 1.64548E-05
2.87959E-05
0
0
8 2.87959E-05
5.75918E-05
5.92731E-11 5.92731E-11
9 4.60735E-05
0.000103665
4.74185E-10 5.33458E-10
10 6.91102E-05
0.000172776
2.13383E-09 2.66729E-09
11 9.87289E-05
0.000271504
7.11277E-09 9.78006E-09
12 0.000135752
0.000407257
1.95601E-08 2.93402E-08
13 0.000181003
0.000588259
4.69443E-08 7.62845E-08
14 0.000235304
0.000823563
1.01713E-07 1.77997E-07
15 0.000299478
0.00112304
2.03425E-07 3.81423E-07
16 0.000374347
0.00149739
3.81423E-07 7.62845E-07
17 0.000460735
0.00195812
6.78084E-07 1.44093E-06
18 0.000559464
0.00251759
1.15274E-06 2.59367E-06
19 0.000671356
0.00318894
1.88631E-06 4.47998E-06
20 0.000797236
0.00398618
2.98665E-06 7.46663E-06
21 0.000937924
0.00492410
4.59485E-06 1.20615E-05
22
0.00109424
0.00601835
6.89228E-06 1.89538E-05
23
0.00126702
0.00728537
1.01087E-05 2.90624E-05
24
0.00145707
0.00874244
1.45312E-05 4.35937E-05
25
0.00166523
0.01040767
2.05147E-05 6.41083E-05
26
0.00189230
0.01229997
2.84926E-05 9.26009E-05
27
0.00213913
0.01443910
3.89899E-05 0.000131591
28
0.00240652
0.01684561
5.26363E-05 0.000184227
29
0.00269530
0.01954091
7.01817E-05 0.000254409
30
0.00300629
0.02254720
9.25123E-05 0.000346921
31
0.00334033
0.02588753
0.000120668 0.000467589
32
0.00369822
0.02958575
0.000155863 0.000623452
33
0.00408079
0.03366654
0.000199505 0.000822957
34
0.00448887
0.03815542
0.000253218 0.00107617
35
0.00492328
0.04307870
0.000318867 0.00139504
36
0.00538484
0.04846353
0.000398583 0.00179362
37
0.00587437
0.05433790
0.000494793 0.00228842
38
0.00639269
0.06073059
0.000610245 0.00289866
39
0.00694064
0.06767123
0.000748042 0.00364670
40
0.00751903
0.07519026
0.000911676 0.00455838
41
0.00812868
0.08331894
0.00110506 0.00566344
42
0.00877041
0.09208935
0.00133257 0.00699602
43
0.00944506
0.10153441
0.00159909 0.00859511
44
0.01015344
0.11168785
0.00191002
0.01050513
45
0.01089638
0.12258423
0.00227138
0.01277651
46
0.01167469
0.13425892
0.00268979
0.01546630
47
0.01248920
0.14674812
0.00317257
0.01863888
48
0.01334074
0.16008886
0.00372778
0.02236665
49
0.01423012
0.17431898
0.00436422
0.02673088
50
0.01515817
0.18947715
0.00509160
0.03182247
51
0.01612571
0.20560286
0.00592046
0.03774293
52
0.01713357
0.22273644
0.00686235
0.04460528
53
0.01818257
0.24091900
0.00792983
0.05253511
54
0.01927352
0.26019252
0.00913654
0.06167165
55
0.02040726
0.28059978
0.01049730
0.07216896
56
0.02158460
0.30218438
0.01202816
0.08419712
57
0.02280637
0.32499074
0.01374647
0.09794358
58
0.02407339
0.34906413
0.01567097
0.11361456
59
0.02538648
0.37445061
0.01782189
0.13143645
60
0.02674647
0.40119709
0.02022099
0.15165744
61
0.02815418
0.42935127
0.02289169
0.17454913
62
0.02961043
0.45896170
0.02585913
0.20040826
63
0.03111605
0.49007775
0.02915029
0.22955855
64
0.03267185
0.52274960
0.03279408
0.26235263
65
0.03427866
0.55702826
0.03682142
0.29917406
66
0.03593731
0.59296557
0.04126539
0.34043944
67
0.03764861
0.63061418
0.04616128
0.38660072
68
0.03941339
0.67002756
0.05154676
0.43814749
69
0.04123247
0.71126003
0.05746197
0.49560945
70
0.04310667
0.75436670
0.06394961
0.55955906
71
0.04503682
0.79940351
0.07105512
0.63061418
72
0.04702374
0.84642725
0.07882677
0.70944095
73
0.04906825
0.89549550
0.08731581
0.79675676
74
0.05117117
0.94666667
0.09657658
0.89333333
75
0.05333333
1
0.10666667 1
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