The 2nd column in the table below shows the single-board probability that all 24 cells (plus the center cell) will be filled when the "Qth" number is called. The 3rd column shows the single-board cumulative probability that all 24 cells (plus the center cell) will be filled on or before the "Qth" number is called.

   If there are 1,000 boards in play, the 4th column in the table below shows the probability that all 24 cells (plus the center cell) will be covered by at least one board when the "Qth" number is called. If there are 1,000 boards in play, the 5th column shows the cumulative probability that at least one board will have a complete cover on or before the time the "Qth" number is called.

For example, when the 64th number is called in a Bingo game, we get the following probabilities:

1) A single board has a 0.00364617 probability of completely covering the board when the 64th number is called.
2) A single board has a 0.00972311 probability of completely covering the board on or before the 64th number.
3) If 1,000 boards are in play, there is a 0.0021959 probability that at least one board will get a complete cover when the 64th number is called.
4) If 1,000 boards are in play, there is a 0.99994 probability that that at least one board will have a complete cover on or before the time the 64th number is called.

(Note, if 1,000 boards are in play, the game will probably end before the 64th number is called.)

To calculate the probability that at least 1 board will be completely covered on or before the "Qth" number is called when "N" boards are in play, go down to the "Qth" row and insert the value for "Cumulative Prob. Complete Cover This Turn 1 Board in the equation:

Prob. of a complete cover with N boards in play = 1.0 - (1.0 - Cum. Prob. 1 board)^N

For example, the probability that at least 1 complete cover will occur on at least 1 board on or before the 60th call when 1000 boards are in play
= 1.0 - (1.0 - 0.00139853)¹⁰⁰⁰
= 0.753283




Quantity    Prob. of a     Cumulative Prob.     Prob. of a     Cumulative Prob.
of Bingo  Complete Cover    Complete Cover    Complete Cover    Complete Cover
Numbers     This  Turn        This  Turn        This  Turn        This  Turn
Picked       1  Board          1  Board        1000  Boards       1000 Boards
-----------------------------------------------------------------------------
   24       3.87917e-20       3.87917e-20       3.87917e-17       3.87917e-17
   25       9.31001e-19       9.69793e-19       9.31001e-16       9.69793e-16
   26       1.16375e-17       1.26073e-17       1.16375e-14       1.26073e-14
   27       1.00858e-16       1.13466e-16       1.00858e-13       1.13466e-13
   28       6.80795e-16        7.9426e-16       6.80795e-13        7.9426e-13
   29       3.81245e-15       4.60671e-15       3.81245e-12       4.60671e-12
   30       1.84268e-14       2.30336e-14       1.84268e-11       2.30336e-11
   31       7.89722e-14       1.02006e-13       7.89722e-11       1.02006e-10
   32       3.06017e-13       4.08023e-13       3.06017e-10       4.08023e-10
   33       1.08806e-12       1.49608e-12       1.08806e-09       1.49608e-09
   34        3.5906e-12       5.08669e-12        3.5906e-09       5.08669e-09
   35       1.10982e-11       1.61849e-11       1.10982e-08       1.61849e-08
   36       3.23698e-11       4.85547e-11       3.23698e-08       4.85547e-08
   37       8.96395e-11       1.38194e-10       8.96395e-08       1.38194e-07
   38       2.36904e-10       3.75099e-10       2.36904e-07       3.75099e-07
   39       6.00158e-10       9.75256e-10       6.00157e-07       9.75256e-07
   40       1.46288e-09       2.43814e-09       1.46288e-06       2.43814e-06
   41       3.44208e-09       5.88022e-09       3.44207e-06        5.8802e-06
   42        7.8403e-09       1.37205e-08       7.84022e-06       1.37204e-05
   43       1.73312e-08       3.10517e-08       1.73308e-05       3.10512e-05
   44        3.7262e-08       6.83137e-08       3.72602e-05       6.83114e-05
   45       7.80728e-08       1.46387e-07       7.80645e-05       0.000146376
   46       1.59694e-07       3.06081e-07       0.000159658       0.000306034
   47       3.19389e-07        6.2547e-07        0.00031924       0.000625275
   48        6.2547e-07       1.25094e-06       0.000624884        0.00125016
   49        1.2009e-06       2.45184e-06        0.00119868        0.00244884
   50       2.26324e-06       4.71508e-06        0.00225515        0.00470399
   51       4.19118e-06       8.90626e-06        0.00416277        0.00886676
   52       7.63394e-06       1.65402e-05        0.00753754         0.0164043
   53       1.36884e-05       3.02287e-05         0.0133725         0.0297768
   54       2.41829e-05       5.44116e-05         0.0231824         0.0529592
   55       4.21251e-05       9.65367e-05         0.0390685         0.0920276
   56       7.24025e-05       0.000168939         0.0634241          0.155452
   57       0.000122865       0.000291804         0.0976651          0.253117
   58       0.000205979       0.000497783          0.139082          0.392199
   59       0.000341337        0.00083912          0.175863          0.568062
   60       0.000559414        0.00139853          0.185221          0.753283
   61       0.000907157        0.00230569          0.147292          0.900575
   62        0.00145623        0.00376192           0.07635          0.976925
   63        0.00231503        0.00607694         0.0208219          0.997747
   64        0.00364617        0.00972311        0.00219592          0.999943
   65        0.00569158         0.0154147       5.69219e-05                 1
   66        0.00880839         0.0242231       1.79184e-07                 1
   67         0.0135199         0.0377429       2.24152e-11                 1
   68         0.0205871           0.05833                 0                 1
   69         0.0311093         0.0894393                 0                 1
   70          0.046664          0.136103                 0                 1
   71         0.0694996          0.205603                 0                 1
   72          0.102801          0.308404                 0                 1
   73          0.151055          0.459459                 0                 1
   74          0.220541              0.68                 0                 1
   75              0.32                 1                 0                 1

Note: Numerical calculations involving large powers (e.g. 1,000) will tend to magnify precision errors. Efforts have been made to reduce precision errors, but results are not guaranteed.

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