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Find P(X) from Binomial Distribution Table

Binomial probability distribution table & how to use instructions to quickly find the probability of x successes from n independent trials in statistics & probability experiments. The Binomial distribution is a discrete probability function often related to trials which involves success or failure.
P(X = x) = P(x) = nCx px q(n-x);
where x = 0, 1, 2, 3 . . . . n
P(x) is 0 otherwise.

Users can refer the below Binomial table or calculator to find the value of P(X). This Binomial-table to find the probability of x successes is also available in pdf format too, users may download this table in pdf format to refer it later offline.

 



Binomial Distribution Table for n = 1 to 10
P 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
 
n = 1   r = 0   0.95  0.9  0.85  0.8  0.75  0.7  0.65  0.6  0.55  0.5 
r = 1   0.05  0.1  0.15  0.2  0.25  0.3  0.35  0.4  0.45  0.5 
 
n = 2   r = 0   0.9025  0.81  0.7225  0.64  0.5625  0.49  0.4225  0.36  0.3025  0.25 
r = 1   0.095  0.18  0.255  0.32  0.375  0.42  0.455  0.48  0.495  0.5 
r = 2   0.0025  0.01  0.0225  0.04  0.0625  0.09  0.1225  0.16  0.2025  0.25 
 
n = 3   r = 0   0.857375  0.729  0.614125  0.512  0.421875  0.343  0.274625  0.216  0.166375  0.125 
r = 1   0.135375  0.243  0.325125  0.384  0.421875  0.441  0.443625  0.432  0.408375  0.375 
r = 2   0.007125  0.027  0.057375  0.096  0.140625  0.189  0.238875  0.288  0.334125  0.375 
r = 3   0.000125  0.001  0.003375  0.008  0.015625  0.027  0.042875  0.064  0.091125  0.125 
 
n = 4   r = 0   0.814506  0.6561  0.522006  0.4096  0.316406  0.2401  0.178506  0.1296  0.091506  0.0625 
r = 1   0.171475  0.2916  0.368475  0.4096  0.421875  0.4116  0.384475  0.3456  0.299475  0.25 
r = 2   0.013538  0.0486  0.097538  0.1536  0.210938  0.2646  0.310538  0.3456  0.367538  0.375 
r = 3   0.000475  0.0036  0.011475  0.0256  0.046875  0.0756  0.111475  0.1536  0.200475  0.25 
r = 4   6.0E-6  0.0001  0.000506  0.0016  0.003906  0.0081  0.015006  0.0256  0.041006  0.0625 
 
n = 5   r = 0   0.773781  0.59049  0.443705  0.32768  0.237305  0.16807  0.116029  0.07776  0.050328  0.03125 
r = 1   0.203627  0.32805  0.391505  0.4096  0.395508  0.36015  0.312386  0.2592  0.205889  0.15625 
r = 2   0.021434  0.0729  0.138178  0.2048  0.263672  0.3087  0.336416  0.3456  0.336909  0.3125 
r = 3   0.001128  0.0081  0.024384  0.0512  0.087891  0.1323  0.181147  0.2304  0.275653  0.3125 
r = 4   3.0E-5  0.00045  0.002152  0.0064  0.014648  0.02835  0.04877  0.0768  0.112767  0.15625 
r = 5   0  1.0E-5  7.6E-5  0.00032  0.000977  0.00243  0.005252  0.01024  0.018453  0.03125 
 
n = 6   r = 0   0.735092  0.531441  0.37715  0.262144  0.177979  0.117649  0.075419  0.046656  0.027681  0.015625 
r = 1   0.232134  0.354294  0.399335  0.393216  0.355957  0.302526  0.243661  0.186624  0.135887  0.09375 
r = 2   0.030544  0.098415  0.176177  0.24576  0.296631  0.324135  0.328005  0.31104  0.27795  0.234375 
r = 3   0.002143  0.01458  0.041453  0.08192  0.131836  0.18522  0.235491  0.27648  0.303218  0.3125 
r = 4   8.5E-5  0.001215  0.005486  0.01536  0.032959  0.059535  0.095102  0.13824  0.186066  0.234375 
r = 5   2.0E-6  5.4E-5  0.000387  0.001536  0.004395  0.010206  0.020484  0.036864  0.060894  0.09375 
r = 6   0  1.0E-6  1.1E-5  6.4E-5  0.000244  0.000729  0.001838  0.004096  0.008304  0.015625 
 
n = 7   r = 0   0.698337  0.478297  0.320577  0.209715  0.133484  0.082354  0.049022  0.027994  0.015224  0.007813 
r = 1   0.257282  0.372009  0.396007  0.367002  0.311462  0.247063  0.184776  0.130637  0.087194  0.054688 
r = 2   0.040623  0.124003  0.209651  0.275251  0.311462  0.317652  0.298485  0.261274  0.214022  0.164063 
r = 3   0.003563  0.022964  0.061662  0.114688  0.173035  0.226895  0.267871  0.290304  0.291848  0.273438 
r = 4   0.000188  0.002552  0.010882  0.028672  0.057678  0.097241  0.144238  0.193536  0.238785  0.273438 
r = 5   6.0E-6  0.00017  0.001152  0.004301  0.011536  0.025005  0.0466  0.077414  0.117221  0.164063 
r = 6   0  6.0E-6  6.8E-5  0.000358  0.001282  0.003572  0.008364  0.017203  0.031969  0.054688 
r = 7   0  0  2.0E-6  1.3E-5  6.1E-5  0.000219  0.000643  0.001638  0.003737  0.007813 
 
n = 8   r = 0   0.66342  0.430467  0.272491  0.167772  0.100113  0.057648  0.031864  0.016796  0.008373  0.003906 
r = 1   0.279335  0.382638  0.384693  0.335544  0.266968  0.19765  0.137262  0.08958  0.054808  0.03125 
r = 2   0.051456  0.148803  0.237604  0.293601  0.311462  0.296475  0.258687  0.209019  0.156949  0.109375 
r = 3   0.005416  0.033067  0.08386  0.146801  0.207642  0.254122  0.278586  0.278692  0.256826  0.21875 
r = 4   0.000356  0.004593  0.018499  0.045875  0.086517  0.136137  0.18751  0.232243  0.262663  0.273438 
r = 5   1.5E-5  0.000408  0.002612  0.009175  0.023071  0.046675  0.080773  0.123863  0.171925  0.21875 
r = 6   0  2.3E-5  0.00023  0.001147  0.003845  0.010002  0.021747  0.041288  0.070333  0.109375 
r = 7   0  1.0E-6  1.2E-5  8.2E-5  0.000366  0.001225  0.003346  0.007864  0.016441  0.03125 
r = 8   0  0  0  3.0E-6  1.5E-5  6.6E-5  0.000225  0.000655  0.001682  0.003906 
 
n = 9   r = 0   0.630249  0.38742  0.231617  0.134218  0.075085  0.040354  0.020712  0.010078  0.004605  0.001953 
r = 1   0.298539  0.38742  0.367862  0.30199  0.225254  0.15565  0.100373  0.060466  0.033912  0.017578 
r = 2   0.06285  0.172187  0.259667  0.30199  0.300339  0.266828  0.216188  0.161243  0.110986  0.070313 
r = 3   0.007718  0.044641  0.106922  0.176161  0.233597  0.266828  0.271621  0.250823  0.211881  0.164063 
r = 4   0.000609  0.00744  0.028303  0.06606  0.116798  0.171532  0.219386  0.250823  0.260036  0.246094 
r = 5   3.2E-5  0.000827  0.004995  0.016515  0.038933  0.073514  0.118131  0.167215  0.212757  0.246094 
r = 6   1.0E-6  6.1E-5  0.000588  0.002753  0.008652  0.021004  0.042406  0.074318  0.116049  0.164063 
r = 7   0  3.0E-6  4.4E-5  0.000295  0.001236  0.003858  0.009786  0.021234  0.040693  0.070313 
r = 8   0  0  2.0E-6  1.8E-5  0.000103  0.000413  0.001317  0.003539  0.008323  0.017578 
r = 9   0  0  0  1.0E-6  4.0E-6  2.0E-5  7.9E-5  0.000262  0.000757  0.001953 
 
n = 10   r = 0   0.598737  0.348678  0.196874  0.107374  0.056314  0.028248  0.013463  0.006047  0.002533  0.000977 
r = 1   0.315125  0.38742  0.347425  0.268435  0.187712  0.121061  0.072492  0.040311  0.020724  0.009766 
r = 2   0.074635  0.19371  0.275897  0.30199  0.281568  0.233474  0.175653  0.120932  0.076303  0.043945 
r = 3   0.010475  0.057396  0.129834  0.201327  0.250282  0.266828  0.25222  0.214991  0.166478  0.117188 
r = 4   0.000965  0.01116  0.040096  0.08808  0.145998  0.200121  0.237668  0.250823  0.238367  0.205078 
r = 5   6.1E-5  0.001488  0.008491  0.026424  0.058399  0.102919  0.15357  0.200658  0.234033  0.246094 
r = 6   3.0E-6  0.000138  0.001249  0.005505  0.016222  0.036757  0.06891  0.111477  0.159568  0.205078 
r = 7   0  9.0E-6  0.000126  0.000786  0.00309  0.009002  0.021203  0.042467  0.074603  0.117188 
r = 8   0  0  8.0E-6  7.4E-5  0.000386  0.001447  0.004281  0.010617  0.02289  0.043945 
r = 9   0  0  0  4.0E-6  2.9E-5  0.000138  0.000512  0.001573  0.004162  0.009766 
r = 10   0  0  0  0  1.0E-6  6.0E-6  2.8E-5  0.000105  0.000341  0.000977 



How to Find P(X) for x Successes from n Trials

Users may use this below Binomial probability table value calculator or refer the rows & columns value of Binomial distribution table to find the probability of x successes from n independent trials.
by Using Calculator
Supply the input values of number of independent trials (n), number of successes (x) & probability (p) directly to the Binomial table value calculator and hit on "LOCATE" to address the corresponding value of P(x).

by Using Binomial Distribution Table
Refer the row for probability (P) value and refer the column value for n & x values. For example, to find the P(x) for n = 2, r = 2 & P = 0.5, the point 0.25 where the row & column meet in the table is the P(x) for the Binomial distribution.

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