Binomial Distribution Table n trials Pr(successes = k)
nkp=0.001p=0.01p=0.05p=0.1p=0.2p=0.3p=0.4p=0.5p=0.6p=0.7p=0.8p=0.9
200.998000.980100.902500.810000.640000.490000.360000.250000.160000.090000.040000.01000
210.002000.019800.095000.180000.320000.420000.480000.500000.480000.420000.320000.18000
220.000000.000100.002500.010000.040000.090000.160000.250000.360000.490000.640000.81000
300.997000.970300.857370.729000.512000.343000.216000.125000.064000.027000.008000.00100
310.002990.029400.135370.243000.384000.441000.432000.375000.288000.189000.096000.02700
320.000000.000300.007130.027000.096000.189000.288000.375000.432000.441000.384000.24300
330.000000.000000.000130.001000.008000.027000.064000.125000.216000.343000.512000.72900
400.996010.960600.814510.656100.409600.240100.129600.062500.025600.008100.001600.00010
410.003990.038810.171470.291600.409600.411600.345600.250000.153600.075600.025600.00360
420.000010.000590.013540.048600.153600.264600.345600.375000.345600.264600.153600.04860
430.000000.000000.000480.003600.025600.075600.153600.250000.345600.411600.409600.29160
440.000000.000000.000010.000100.001600.008100.025600.062500.129600.240100.409600.65610
500.995010.950990.773780.590490.327680.168070.077760.031250.010240.002430.000320.00001
510.004980.048030.203630.328050.409600.360150.259200.156250.076800.028350.006400.00045
520.000010.000970.021430.072900.204800.308700.345600.312500.230400.132300.051200.00810
530.000000.000010.001130.008100.051200.132300.230400.312500.345600.308700.204800.07290
540.000000.000000.000030.000450.006400.028350.076800.156250.259200.360150.409600.32805
550.000000.000000.000000.000010.000320.002430.010240.031250.077760.168070.327680.59049
600.994010.941480.735090.531440.262140.117650.046660.015620.004100.000730.000060.00000
610.005970.057060.232130.354290.393220.302530.186620.093750.036860.010210.001540.00005
620.000010.001440.030540.098420.245760.324130.311040.234380.138240.059540.015360.00121
630.000000.000020.002140.014580.081920.185220.276480.312500.276480.185220.081920.01458
640.000000.000000.000080.001220.015360.059530.138240.234380.311040.324140.245760.09841
650.000000.000000.000000.000050.001540.010210.036860.093750.186620.302530.393220.35429
660.000000.000000.000000.000000.000060.000730.004100.015620.046660.117650.262140.53144
700.993020.932070.698340.478300.209720.082350.027990.007810.001640.000220.000010.00000
710.006960.065900.257280.372010.367000.247060.130640.054690.017200.003570.000360.00001
720.000020.002000.040620.124000.275250.317650.261270.164060.077410.025000.004300.00017
730.000000.000030.003560.022960.114690.226890.290300.273440.193540.097240.028670.00255
740.000000.000000.000190.002550.028670.097240.193540.273440.290300.226890.114690.02296
750.000000.000000.000010.000170.004300.025000.077410.164060.261270.317650.275250.12400
760.000000.000000.000000.000010.000360.003570.017200.054690.130640.247060.367000.37201
770.000000.000000.000000.000000.000010.000220.001640.007810.027990.082350.209720.47830
800.992030.922740.663420.430470.167770.057650.016800.003910.000660.000070.000000.00000
810.007940.074570.279330.382640.335540.197650.089580.031250.007860.001220.000080.00000
820.000030.002640.051460.148800.293600.296480.209020.109380.041290.010000.001150.00002
830.000000.000050.005420.033070.146800.254120.278690.218750.123860.046680.009180.00041
840.000000.000000.000360.004590.045880.136140.232240.273440.232240.136140.045880.00459
850.000000.000000.000020.000410.009180.046680.123860.218750.278690.254120.146800.03307
860.000000.000000.000000.000020.001150.010000.041290.109380.209020.296480.293600.14880
870.000000.000000.000000.000000.000080.001220.007860.031250.089580.197650.335540.38264
880.000000.000000.000000.000000.000000.000070.000660.003910.016800.057650.167770.43047
900.991040.913520.630250.387420.134220.040350.010080.001950.000260.000020.000000.00000
910.008930.083050.298540.387420.301990.155650.060470.017580.003540.000410.000020.00000
920.000040.003360.062850.172190.301990.266830.161240.070310.021230.003860.000290.00000
930.000000.000080.007720.044640.176160.266830.250820.164060.074320.021000.002750.00006
940.000000.000000.000610.007440.066060.171530.250820.246090.167220.073510.016520.00083
950.000000.000000.000030.000830.016520.073510.167220.246090.250820.171530.066060.00744
960.000000.000000.000000.000060.002750.021000.074320.164060.250820.266830.176160.04464
970.000000.000000.000000.000000.000290.003860.021230.070310.161240.266830.301990.17219
980.000000.000000.000000.000000.000020.000410.003540.017580.060470.155650.301990.38742
990.000000.000000.000000.000000.000000.000020.000260.001950.010080.040350.134220.38742
1000.990040.904380.598740.348680.107370.028250.006050.000980.000100.000010.000000.00000
1010.009910.091350.315120.387420.268440.121060.040310.009770.001570.000140.000000.00000
1020.000040.004150.074630.193710.301990.233470.120930.043950.010620.001450.000070.00000
1030.000000.000110.010480.057400.201330.266830.214990.117190.042470.009000.000790.00001
1040.000000.000000.000960.011160.088080.200120.250820.205080.111480.036760.005510.00014
1050.000000.000000.000060.001490.026420.102920.200660.246090.200660.102920.026420.00149
1060.000000.000000.000000.000140.005510.036760.111480.205080.250820.200120.088080.01116
1070.000000.000000.000000.000010.000790.009000.042470.117190.214990.266830.201330.05740
1080.000000.000000.000000.000000.000070.001450.010620.043950.120930.233470.301990.19371
1090.000000.000000.000000.000000.000000.000140.001570.009770.040310.121060.268440.38742
10100.000000.000000.000000.000000.000000.000010.000100.000980.006050.028250.107370.34868
1100.989050.895340.568800.313810.085900.019770.003630.000490.000040.000000.000000.00000
1110.010890.099480.329310.383550.236220.093220.026610.005370.000690.000050.000000.00000
1120.000050.005020.086660.213080.295280.199750.088680.026860.005190.000530.000020.00000
1130.000000.000150.013680.071030.221460.256820.177370.080570.023360.003710.000220.00000
1140.000000.000000.001440.015780.110730.220130.236490.161130.070070.017330.001730.00002
1150.000000.000000.000110.002460.038760.132080.220720.225590.147150.056610.009690.00027
1160.000000.000000.000010.000270.009690.056610.147150.225590.220720.132080.038760.00246
1170.000000.000000.000000.000020.001730.017330.070070.161130.236490.220130.110730.01578
1180.000000.000000.000000.000000.000220.003710.023360.080570.177370.256820.221460.07103
1190.000000.000000.000000.000000.000020.000530.005190.026860.088680.199750.295280.21308
11100.000000.000000.000000.000000.000000.000050.000690.005370.026610.093220.236220.38355
11110.000000.000000.000000.000000.000000.000000.000040.000490.003630.019770.085900.31381
1200.988070.886380.540360.282430.068720.013840.002180.000240.000020.000000.000000.00000
1210.011870.107440.341280.376570.206160.071180.017410.002930.000300.000010.000000.00000
1220.000070.005970.098790.230130.283470.167790.063850.016110.002490.000190.000000.00000
1230.000000.000200.017330.085230.236220.239700.141890.053710.012460.001490.000060.00000
1240.000000.000000.002050.021310.132880.231140.212840.120850.042040.007800.000520.00000
1250.000000.000000.000170.003790.053150.158500.227030.193360.100900.029110.003320.00005
1260.000000.000000.000010.000490.015500.079250.176580.225590.176580.079250.015500.00049
1270.000000.000000.000000.000050.003320.029110.100900.193360.227030.158500.053150.00379
1280.000000.000000.000000.000000.000520.007800.042040.120850.212840.231140.132880.02131
1290.000000.000000.000000.000000.000060.001490.012460.053710.141890.239700.236220.08523
12100.000000.000000.000000.000000.000000.000190.002490.016110.063850.167790.283470.23013
12110.000000.000000.000000.000000.000000.000010.000300.002930.017410.071180.206160.37657
12120.000000.000000.000000.000000.000000.000000.000020.000240.002180.013840.068720.28243
1300.987080.877520.513340.254190.054980.009690.001310.000120.000010.000000.000000.00000
1310.012840.115230.351230.367160.178670.053980.011320.001590.000130.000000.000000.00000
1320.000080.006980.110920.244770.268010.138810.045280.009520.001180.000070.000000.00000
1330.000000.000260.021400.099720.245670.218130.110680.034910.006480.000580.000010.00000
1340.000000.000010.002820.027700.153550.233710.184460.087280.024290.003380.000150.00000
1350.000000.000000.000270.005540.069100.180290.221350.157100.065590.014190.001080.00001
1360.000000.000000.000020.000820.023030.103020.196760.209470.131170.044150.005760.00009
1370.000000.000000.000000.000090.005760.044150.131170.209470.196760.103020.023030.00082
1380.000000.000000.000000.000010.001080.014190.065590.157100.221350.180290.069100.00554
1390.000000.000000.000000.000000.000150.003380.024290.087280.184460.233710.153550.02770
13100.000000.000000.000000.000000.000010.000580.006480.034910.110680.218130.245670.09972
13110.000000.000000.000000.000000.000000.000070.001180.009520.045280.138810.268010.24477
13120.000000.000000.000000.000000.000000.000000.000130.001590.011320.053980.178670.36716
13130.000000.000000.000000.000000.000000.000000.000010.000120.001310.009690.054980.25419
1400.986090.868750.487670.228770.043980.006780.000780.000060.000000.000000.000000.00000
1410.013820.122850.359340.355860.153930.040690.007310.000850.000060.000000.000000.00000
1420.000090.008070.122930.257010.250140.113360.031690.005550.000550.000020.000000.00000
1430.000000.000330.025880.114230.250140.194330.084520.022220.003300.000220.000000.00000
1440.000000.000010.003750.034900.171970.229030.154950.061100.013600.001420.000040.00000
1450.000000.000000.000390.007760.085990.196310.206600.122190.040810.006620.000340.00000
1460.000000.000000.000030.001290.032240.126200.206600.183290.091820.023180.002020.00002
1470.000000.000000.000000.000160.009210.061810.157410.209470.157410.061810.009210.00016
1480.000000.000000.000000.000020.002020.023180.091820.183290.206600.126200.032240.00129
1490.000000.000000.000000.000000.000340.006620.040810.122190.206600.196310.085990.00776
14100.000000.000000.000000.000000.000040.001420.013600.061100.154950.229030.171970.03490
14110.000000.000000.000000.000000.000000.000220.003300.022220.084520.194330.250140.11423
14120.000000.000000.000000.000000.000000.000020.000550.005550.031690.113360.250140.25701
14130.000000.000000.000000.000000.000000.000000.000060.000850.007310.040690.153930.35586
14140.000000.000000.000000.000000.000000.000000.000000.000060.000780.006780.043980.22877
1500.985100.860060.463290.205890.035180.004750.000470.000030.000000.000000.000000.00000
1510.014790.130310.365760.343150.131940.030520.004700.000460.000020.000000.000000.00000
1520.000100.009210.134750.266900.230900.091560.021940.003200.000250.000010.000000.00000
1530.000000.000400.030730.128510.250140.170040.063390.013890.001650.000080.000000.00000
1540.000000.000010.004850.042840.187600.218620.126780.041660.007420.000580.000010.00000
1550.000000.000000.000560.010470.103180.206130.185940.091640.024490.002980.000100.00000
1560.000000.000000.000050.001940.042990.147240.206600.152740.061210.011590.000670.00000
1570.000000.000000.000000.000280.013820.081130.177080.196380.118060.034770.003450.00003
1580.000000.000000.000000.000030.003450.034770.118060.196380.177080.081130.013820.00028
1590.000000.000000.000000.000000.000670.011590.061210.152740.206600.147240.042990.00194
15100.000000.000000.000000.000000.000100.002980.024490.091640.185940.206130.103180.01047
15110.000000.000000.000000.000000.000010.000580.007420.041660.126780.218620.187600.04284
15120.000000.000000.000000.000000.000000.000080.001650.013890.063390.170040.250140.12851
15130.000000.000000.000000.000000.000000.000010.000250.003200.021940.091560.230900.26690
15140.000000.000000.000000.000000.000000.000000.000020.000460.004700.030520.131940.34315
15150.000000.000000.000000.000000.000000.000000.000000.000030.000470.004750.035180.20589
1600.984120.851460.440130.185300.028150.003320.000280.000020.000000.000000.000000.00000
1610.015760.137610.370630.329430.112590.022790.003010.000240.000010.000000.000000.00000
1620.000120.010420.146300.274520.211110.073250.015050.001830.000120.000000.000000.00000
1630.000000.000490.035930.142340.246290.146500.046810.008540.000810.000030.000000.00000
1640.000000.000020.006150.051400.200110.204050.101420.027770.003960.000230.000000.00000
1650.000000.000000.000780.013710.120070.209880.162270.066650.014250.001300.000030.00000
1660.000000.000000.000070.002790.055030.164900.198330.122190.039180.005560.000210.00000
1670.000000.000000.000010.000440.019650.100960.188890.174560.083950.018540.001230.00001
1680.000000.000000.000000.000060.005530.048680.141670.196380.141670.048680.005530.00006
1690.000000.000000.000000.000010.001230.018540.083950.174560.188890.100960.019650.00044
16100.000000.000000.000000.000000.000210.005560.039180.122190.198330.164900.055030.00279
16110.000000.000000.000000.000000.000030.001300.014250.066650.162270.209880.120070.01371
16120.000000.000000.000000.000000.000000.000230.003960.027770.101420.204050.200110.05140
16130.000000.000000.000000.000000.000000.000030.000810.008540.046810.146500.246290.14234
16140.000000.000000.000000.000000.000000.000000.000120.001830.015050.073250.211110.27452
16150.000000.000000.000000.000000.000000.000000.000010.000240.003010.022790.112590.32943
16160.000000.000000.000000.000000.000000.000000.000000.000020.000280.003320.028150.18530
1700.983140.842940.418120.166770.022520.002330.000170.000010.000000.000000.000000.00000
1710.016730.144750.374110.315010.095700.016950.001920.000130.000000.000000.000000.00000
1720.000130.011700.157520.280010.191400.058110.010230.001040.000050.000000.000000.00000
1730.000000.000590.041450.155560.239250.124520.034100.005190.000390.000010.000000.00000
1740.000000.000020.007640.060500.209350.186780.079580.018160.002070.000090.000000.00000
1750.000000.000000.001040.017480.136080.208130.137930.047210.008070.000550.000010.00000
1760.000000.000000.000110.003880.068040.178400.183910.094420.024220.002580.000070.00000
1770.000000.000000.000010.000680.026730.120140.192670.148380.057090.009460.000420.00000
1780.000000.000000.000000.000090.008350.064360.160560.185470.107040.027580.002090.00001
1790.000000.000000.000000.000010.002090.027580.107040.185470.160560.064360.008350.00009
17100.000000.000000.000000.000000.000420.009460.057090.148380.192670.120140.026730.00068
17110.000000.000000.000000.000000.000070.002580.024220.094420.183910.178400.068040.00388
17120.000000.000000.000000.000000.000010.000550.008070.047210.137930.208130.136080.01748
17130.000000.000000.000000.000000.000000.000090.002070.018160.079580.186780.209350.06050
17140.000000.000000.000000.000000.000000.000010.000390.005190.034100.124520.239250.15556
17150.000000.000000.000000.000000.000000.000000.000050.001040.010230.058110.191400.28001
17160.000000.000000.000000.000000.000000.000000.000000.000130.001920.016950.095700.31501
17170.000000.000000.000000.000000.000000.000000.000000.000010.000170.002330.022520.16677
1800.982150.834510.397210.150090.018010.001630.000100.000000.000000.000000.000000.00000
1810.017700.151730.376310.300190.081060.012560.001220.000070.000000.000000.000000.00000
1820.000150.013030.168350.283510.172260.045760.006910.000580.000020.000000.000000.00000
1830.000000.000700.047260.168010.229680.104600.024550.003110.000190.000000.000000.00000
1840.000000.000030.009330.070000.215330.168100.061390.011670.001060.000040.000000.00000
1850.000000.000000.001370.021780.150730.201730.114590.032680.004470.000230.000000.00000
1860.000000.000000.000160.005240.081650.187320.165520.070820.014530.001160.000020.00000
1870.000000.000000.000010.001000.034990.137620.189160.121400.037370.004640.000140.00000
1880.000000.000000.000000.000150.012030.081100.173400.166920.077070.014900.000750.00000
1890.000000.000000.000000.000020.003340.038620.128440.185470.128440.038620.003340.00002
18100.000000.000000.000000.000000.000750.014900.077070.166920.173400.081100.012030.00015
18110.000000.000000.000000.000000.000140.004640.037370.121400.189160.137620.034990.00100
18120.000000.000000.000000.000000.000020.001160.014530.070820.165520.187320.081650.00524
18130.000000.000000.000000.000000.000000.000230.004470.032680.114590.201730.150730.02178
18140.000000.000000.000000.000000.000000.000040.001060.011670.061390.168100.215330.07000
18150.000000.000000.000000.000000.000000.000000.000190.003110.024550.104600.229680.16801
18160.000000.000000.000000.000000.000000.000000.000020.000580.006910.045760.172260.28351
18170.000000.000000.000000.000000.000000.000000.000000.000070.001220.012560.081060.30019
18180.000000.000000.000000.000000.000000.000000.000000.000000.000100.001630.018010.15009
1900.981170.826170.377350.135090.014410.001140.000060.000000.000000.000000.000000.00000
1910.018660.158560.377350.285180.068450.009280.000770.000040.000000.000000.000000.00000
1920.000170.014410.178750.285180.154020.035800.004630.000330.000010.000000.000000.00000
1930.000000.000830.053310.179560.218200.086950.017500.001850.000090.000000.000000.00000
1940.000000.000030.011220.079800.218200.149050.046650.007390.000540.000010.000000.00000
1950.000000.000000.001770.026600.163650.191640.093310.022180.002430.000090.000000.00000
1960.000000.000000.000220.006900.095460.191640.145150.051750.008500.000510.000010.00000
1970.000000.000000.000020.001420.044320.152530.179710.096110.023660.002210.000040.00000
1980.000000.000000.000000.000240.016620.098050.179710.144160.053250.007720.000260.00000
1990.000000.000000.000000.000030.005080.051360.146430.176200.097620.022010.001270.00000
19100.000000.000000.000000.000000.001270.022010.097620.176200.146430.051360.005080.00003
19110.000000.000000.000000.000000.000260.007720.053250.144160.179710.098050.016620.00024
19120.000000.000000.000000.000000.000040.002210.023660.096110.179710.152530.044320.00142
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3