MicrobiologyBytes: Maths & Computers for Biologists: Binomial probabilities Search

Table of Binomial Probabilities

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p
n s .01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
2 0 .980 .960 .922 .903 .884 .846 .810 .774 .740 .723 .706 .672 .640 .608 .578 .563 .490 .423 .360 .303 .250
2 1 .020 .039 .077 .095 .113 .147 .180 .211 .241 .255 .269 .295 .320 .343 .365 .375 .420 .455 .480 .495 .500
2 2     .002 .003 .004 .006 .010 .014 .020 .023 .026 .032 .040 .048 .058 .063 .090 .123 .160 .203 .250
3 0 .970 .941 .885 .857 .831 .779 .729 .681 .636 .614 .593 .551 .512 .475 .439 .422 .343 .275 .216 .166 .125
3 1 .029 .058 .111 .135 .159 .203 .243 .279 .311 .325 .339 .363 .384 .402 .416 .422 .441 .444 .432 .408 .375
3 2   .001 .005 .007 .010 .018 .027 .038 .051 .057 .065 .080 .096 .113 .131 .141 .189 .239 .288 .334 .375
3 3           .001 .001 .002 .003 .003 .004 .006 .008 .011 .014 .016 .027 .043 .064 .091 .125
4 0 .961 .922 .849 .815 .781 .716 .656 .600 .547 .522 .498 .452 .410 .370 .334 .316 .240 .179 .130 .092 .063
4 1 .039 .075 .142 .171 .199 .249 .292 .327 .356 .368 .379 .397 .410 .418 .421 .422 .412 .384 .346 .299 .250
4 2 .001 .002 .009 .014 .019 .033 .049 .067 .087 .098 .108 .131 .154 .177 .200 .211 .265 .311 .346 .368 .375
4 3         .001 .002 .004 .006 .009 .011 .014 .019 .026 .033 .042 .047 .076 .111 .154 .200 .250
4 4                   .001 .001 .001 .002 .002 .003 .004 .008 .015 .026 .041 .063
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
5 0 .951 .904 .815 .774 .734 .659 .590 .528 .470 .444 .418 .371 .328 .289 .254 .237 .168 .116 .078 .050 .031
5 1 .048 .092 .170 .204 .234 .287 .328 .360 .383 .392 .398 .407 .410 .407 .400 .396 .360 .312 .259 .206 .156
5 2 .001 .004 .014 .021 .030 .050 .073 .098 .125 .138 .152 .179 .205 .230 .253 .264 .309 .336 .346 .337 .313
5 3     .001 .001 .002 .004 .008 .013 .020 .024 .029 .039 .051 .065 .080 .088 .132 .181 .230 .276 .313
5 4               .001 .002 .002 .003 .004 .006 .009 .013 .015 .028 .049 .077 .113 .156
5 5                           .001 .001 .001 .002 .005 .010 .018 .031
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
6 0 .941 .886 .783 .735 .690 .606 .531 .464 .405 .377 .351 .304 .262 .225 .193 .178 .118 .075 .047 .028 .016
6 1 .057 .108 .196 .232 .264 .316 .354 .380 .395 .399 .401 .400 .393 .381 .365 .356 .303 .244 .187 .136 .094
6 2 .001 .006 .020 .031 .042 .069 .098 .130 .161 .176 .191 .220 .246 .269 .288 .297 .324 .328 .311 .278 .234
6 3     .001 .002 .004 .008 .015 .024 .035 .041 .049 .064 .082 .101 .121 .132 .185 .235 .276 .303 .313
6 4           .001 .001 .002 .004 .005 .007 .011 .015 .021 .029 .033 .060 .095 .138 .186 .234
6 5                     .001 .001 .002 .002 .004 .004 .010 .020 .037 .061 .094
6 6                                 .001 .002 .004 .008 .016
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
7 0 .932 .868 .751 .698 .648 .558 .478 .409 .348 .321 .295 .249 .210 .176 .146 .133 .082 .049 .028 .015 .008
7 1 .066 .124 .219 .257 .290 .340 .372 .390 .396 .396 .393 .383 .367 .347 .324 .311 .247 .185 .131 .087 .055
7 2 .002 .008 .027 .041 .055 .089 .124 .160 .194 .210 .225 .252 .275 .293 .307 .311 .318 .298 .261 .214 .164
7 3     .002 .004 .006 .013 .023 .036 .053 .062 .071 .092 .115 .138 .161 .173 .227 .268 .290 .292 .273
7 4           .001 .003 .005 .009 .011 .014 .020 .029 .039 .051 .058 .097 .144 .194 .239 .273
7 5                 .001 .001 .002 .003 .004 .007 .010 .012 .025 .047 .077 .117 .164
7 6                           .001 .001 .001 .004 .008 .017 .032 .055
7 7                                   .001 .002 .004 .008
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
8 0 .923 .851 .721 .663 .610 .513 .430 .360 .299 .272 .248 .204 .168 .137 .111 .100 .058 .032 .017 .008 .004
8 1 .075 .139 .240 .279 .311 .357 .383 .392 .390 .385 .378 .359 .336 .309 .281 .267 .198 .137 .090 .055 .031
8 2 .003 .010 .035 .051 .070 .109 .149 .187 .222 .238 .252 .276 .294 .305 .311 .311 .296 .259 .209 .157 .109
8 3     .003 .005 .009 .019 .033 .051 .072 .084 .096 .121 .147 .172 .196 .208 .254 .279 .279 .257 .219
8 4         .001 .002 .005 .009 .015 .018 .023 .033 .046 .061 .077 .087 .136 .188 .232 .263 .273
8 5               .001 .002 .003 .003 .006 .009 .014 .020 .023 .047 .081 .124 .172 .219
8 6                       .001 .001 .002 .003 .004 .010 .022 .041 .070 .109
8 7                                 .001 .003 .008 .016 .031
8 8                                     .001 .002 .004
9 0 .914 .834 .693 .630 .573 .472 .387 .316 .257 .232 .208 .168 .134 .107 .085 .075 .040 .021 .010 .005 .002
9 1 .083 .153 .260 .299 .329 .370 .387 .388 .377 .368 .357 .331 .302 .271 .240 .225 .156 .100 .060 .034 .018
9 2 .003 .013 .043 .063 .084 .129 .172 .212 .245 .260 .272 .291 .302 .306 .304 .300 .267 .216 .161 .111 .070
9 3   .001 .004 .008 .013 .026 .045 .067 .093 .107 .121 .149 .176 .201 .224 .234 .267 .272 .251 .212 .164
9 4       .001 .001 .003 .007 .014 .023 .028 .035 .049 .066 .085 .106 .117 .172 .219 .251 .260 .246
9 5             .001 .002 .004 .005 .007 .011 .017 .024 .033 .039 .074 .118 .167 .213 .246
9 6                   .001 .001 .002 .003 .005 .007 .009 .021 .042 .074 .116 .164
9 7                           .001 .001 .001 .004 .010 .021 .041 .070
9 8                                   .001 .004 .008 .018
9 9                                       .001 .002
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
10 0 .904 .817 .665 .599 .539 .434 .349 .279 .221 .197 .175 .137 .107 .083 .064 .056 .028 .013 .006 .003 .001
10 1 .091 .167 .277 .315 .344 .378 .387 .380 .360 .347 .333 .302 .268 .235 .203 .188 .121 .072 .040 .021 .010
10 2 .004 .015 .052 .075 .099 .148 .194 .233 .264 .276 .286 .298 .302 .298 .288 .282 .233 .176 .121 .076 .044
10 3   .001 .006 .010 .017 .034 .057 .085 .115 .130 .145 .174 .201 .224 .243 .250 .267 .252 .215 .166 .117
10 4       .001 .002 .005 .011 .020 .033 .040 .048 .067 .088 .111 .134 .146 .200 .238 .251 .238 .205
10 5           .001 .001 .003 .006 .008 .011 .018 .026 .037 .051 .058 .103 .154 .201 .234 .246
10 6                 .001 .001 .002 .003 .006 .009 .013 .016 .037 .069 .111 .160 .205
10 7                         .001 .001 .002 .003 .009 .021 .042 .075 .117
10 8                                 .001 .004 .011 .023 .044
10 9                                   .001 .002 .004 .010
10 10                                         .001
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
11 0 .895 .801 .638 .569 .506 .400 .314 .245 .190 .167 .147 .113 .086 .065 .049 .042 .020 .009 .004 .001  
11 1 .099 .180 .293 .329 .355 .382 .384 .368 .341 .325 .308 .272 .236 .202 .170 .155 .093 .052 .027 .013 .005
11 2 .005 .018 .061 .087 .113 .166 .213 .251 .277 .287 .293 .299 .295 .284 .268 .258 .200 .140 .089 .051 .027
11 3   .001 .008 .014 .022 .043 .071 .103 .135 .152 .168 .197 .221 .241 .254 .258 .257 .225 .177 .126 .081
11 4     .001 .001 .003 .008 .016 .028 .044 .054 .064 .086 .111 .136 .160 .172 .220 .243 .236 .206 .161
11 5           .001 .002 .005 .010 .013 .017 .027 .039 .054 .071 .080 .132 .183 .221 .236 .226
11 6               .001 .002 .002 .003 .006 .010 .015 .022 .027 .057 .099 .147 .193 .226
11 7                       .001 .002 .003 .005 .006 .017 .038 .070 .113 .161
11 8                             .001 .001 .004 .010 .023 .046 .081
11 9                                 .001 .002 .005 .013 .027
11 10                                     .001 .002 .005
11 11                                          
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
12 0 .886 .785 .613 .540 .476 .368 .282 .216 .164 .142 .123 .092 .069 .051 .037 .032 .014 .006 .002 .001  
12 1 .107 .192 .306 .341 .365 .384 .377 .353 .320 .301 .282 .243 .206 .172 .141 .127 .071 .037 .017 .008 .003
12 2 .006 .022 .070 .099 .128 .183 .230 .265 .286 .292 .296 .294 .283 .266 .244 .232 .168 .109 .064 .034 .016
12 3   .001 .010 .017 .027 .053 .085 .120 .155 .172 .188 .215 .236 .250 .257 .258 .240 .195 .142 .092 .054
12 4     .001 .002 .004 .010 .021 .037 .057 .068 .080 .106 .133 .159 .183 .194 .231 .237 .213 .170 .121
12 5           .001 .004 .008 .015 .019 .025 .037 .053 .072 .092 .103 .158 .204 .227 .222 .193
12 6               .001 .003 .004 .005 .010 .016 .024 .034 .040 .079 .128 .177 .212 .226
12 7                   .001 .001 .002 .003 .006 .009 .011 .029 .059 .101 .149 .193
12 8                         .001 .001 .002 .002 .008 .020 .042 .076 .121
12 9                                 .001 .005 .012 .028 .054
12 10                                   .001 .002 .007 .016
12 11                                       .001 .003
12 12                                          
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
13 0 .878 .769 .588 .513 .447 .338 .254 .190 .141 .121 .104 .076 .055 .040 .028 .024 .010 .004 .001    
13 1 .115 .204 .319 .351 .371 .382 .367 .336 .298 .277 .257 .216 .179 .145 .116 .103 .054 .026 .011 .004 .002
13 2 .007 .025 .080 .111 .142 .199 .245 .275 .291 .294 .293 .285 .268 .245 .220 .206 .139 .084 .045 .022 .010
13 3   .002 .012 .021 .033 .064 .100 .138 .174 .190 .205 .229 .246 .254 .254 .252 .218 .165 .111 .066 .035
13 4     .001 .003 .005 .014 .028 .047 .071 .084 .098 .126 .154 .179 .201 .210 .234 .222 .184 .135 .087
13 5         .001 .002 .006 .012 .021 .027 .033 .050 .069 .091 .114 .126 .180 .215 .221 .199 .157
13 6             .001 .002 .004 .006 .008 .015 .023 .034 .048 .056 .103 .155 .197 .217 .209
13 7                 .001 .001 .002 .003 .006 .010 .015 .019 .044 .083 .131 .177 .209
13 8                       .001 .001 .002 .004 .005 .014 .034 .066 .109 .157
13 9                             .001 .001 .003 .010 .024 .050 .087
13 10                                 .001 .002 .006 .016 .035
13 11                                     .001 .004 .010
13 12                                         .002
13 13                                          
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
14 0 .869 .754 .565 .488 .421 .311 .229 .167 .121 .103 .087 .062 .044 .031 .021 .018 .007 .002 .001    
14 1 .123 .215 .329 .359 .376 .379 .356 .319 .276 .254 .232 .191 .154 .122 .095 .083 .041 .018 .007 .003 .001
14 2 .008 .029 .089 .123 .156 .214 .257 .283 .292 .291 .287 .272 .250 .223 .195 .180 .113 .063 .032 .014 .006
14 3   .002 .015 .026 .040 .074 .114 .154 .190 .206 .219 .239 .250 .252 .246 .240 .194 .137 .085 .046 .022
14 4     .002 .004 .007 .018 .035 .058 .085 .100 .115 .144 .172 .195 .214 .220 .229 .202 .155 .104 .061
14 5         .001 .003 .008 .016 .028 .035 .044 .063 .086 .110 .135 .147 .196 .218 .207 .170 .122
14 6             .001 .003 .007 .009 .012 .021 .032 .047 .064 .073 .126 .176 .207 .209 .183
14 7               .001 .001 .002 .003 .005 .009 .015 .023 .028 .062 .108 .157 .195 .209
14 8                       .001 .002 .004 .006 .008 .023 .051 .092 .140 .183
14 9                           .001 .001 .002 .007 .018 .041 .076 .122
14 10                                 .001 .005 .014 .031 .061
14 11                                   .001 .003 .009 .022
14 12                                     .001 .002 .006
14 13                                         .001
14 14                                          
.01 .02 .04 .05 .06 .08 .10 .12 .14 .15 .16 .18 .20 .22 .24 .25 .30 .35 .40 .45 .50
15 0 .860 .739 .542 .463 .395 .286 .206 .147 .104 .087 .073 .051 .035 .024 .016 .013 .005 .002      
15 1 .130 .226 .339 .366 .378 .373 .343 .301 .254 .231 .209 .168 .132 .102 .077 .067 .031 .013 .005 .002  
15 2 .009 .032 .099 .135 .169 .227 .267 .287 .290 .286 .279 .258 .231 .201 .171 .156 .092 .048 .022 .009 .003
15 3   .003 .018 .031 .047 .086 .129 .170 .204 .218 .230 .245 .250 .246 .234 .225 .170 .111 .063 .032 .014
15 4     .002 .005 .009 .022 .043 .069 .100 .116 .131 .162 .188 .208 .221 .225 .219 .179 .127 .078 .042
15 5       .001 .001 .004 .010 .021 .036 .045 .055 .078 .103 .129 .154 .165 .206 .212 .186 .140 .092
15 6           .001 .002 .005 .010 .013 .017 .029 .043 .061 .081 .092 .147 .191 .207 .191 .153
15 7               .001 .002 .003 .004 .008 .014 .022 .033 .039 .081 .132 .177 .201 .196
15 8                   .001 .001 .002 .003 .006 .010 .013 .035 .071 .118 .165 .196
15 9                         .001 .001 .003 .003 .012 .030 .061 .105 .153
15 10                               .001 .003 .010 .024 .051 .092
15 11                                 .001 .002 .007 .019 .042
15 12                                     .002 .005 .014
15 13                                       .001 .003
15 14                                          
15 15                                          

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