MicrobiologyBytes: Maths & Computers for Biologists: Binomial probabilities

Table of Binomial Probabilities

Use the BACK button to return to the previous page.

The following table lists the probability of attaining s successes out of n trials, where the probability of success in any one trial is p

To find the probability of obtaining s or more successes in n trials, add the probabilities corresponding to s, s+1, s+2,... together. For example, the probability of obtaining 1 or more heads in two coin flips is 0.500 + 0.250 = 0.750

If p is greater than .5, then use 1-p as the probability and n-s as the desired number of successes (i.e. look up the probability of obtaining n-s failures rather than s successes).

		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

Use the BACK button to return to the previous page.