Statistical Tables/Binomial Probability Table

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Binomial Probability Table

Look up binomial probabilities the way you would in the back of a textbook, for common values of n and p.

Number of trials (n)

Table shows

n = 10, P(X = k) for each success probability p

k	0.05	0.1	0.15	0.2	0.25	0.3	0.35	0.4	0.45	0.5	0.6	0.7	0.75	0.8	0.85	0.9	0.95
0	0.5987	0.3487	0.1969	0.1074	0.0563	0.0282	0.0135	0.006	0.0025	0.001	0.0001	0	0	0	0	0	0
1	0.3151	0.3874	0.3474	0.2684	0.1877	0.1211	0.0725	0.0403	0.0207	0.0098	0.0016	0.0001	0	0	0	0	0
2	0.0746	0.1937	0.2759	0.302	0.2816	0.2335	0.1757	0.1209	0.0763	0.0439	0.0106	0.0014	0.0004	0.0001	0	0	0
3	0.0105	0.0574	0.1298	0.2013	0.2503	0.2668	0.2522	0.215	0.1665	0.1172	0.0425	0.009	0.0031	0.0008	0.0001	0	0
4	0.001	0.0112	0.0401	0.0881	0.146	0.2001	0.2377	0.2508	0.2384	0.2051	0.1115	0.0368	0.0162	0.0055	0.0012	0.0001	0
5	0.0001	0.0015	0.0085	0.0264	0.0584	0.1029	0.1536	0.2007	0.234	0.2461	0.2007	0.1029	0.0584	0.0264	0.0085	0.0015	0.0001
6	0	0.0001	0.0012	0.0055	0.0162	0.0368	0.0689	0.1115	0.1596	0.2051	0.2508	0.2001	0.146	0.0881	0.0401	0.0112	0.001
7	0	0	0.0001	0.0008	0.0031	0.009	0.0212	0.0425	0.0746	0.1172	0.215	0.2668	0.2503	0.2013	0.1298	0.0574	0.0105
8	0	0	0	0.0001	0.0004	0.0014	0.0043	0.0106	0.0229	0.0439	0.1209	0.2335	0.2816	0.302	0.2759	0.1937	0.0746
9	0	0	0	0	0	0.0001	0.0005	0.0016	0.0042	0.0098	0.0403	0.1211	0.1877	0.2684	0.3474	0.3874	0.3151
10	0	0	0	0	0	0	0	0.0001	0.0003	0.001	0.006	0.0282	0.0563	0.1074	0.1969	0.3487	0.5987

Each column is a different success probability p. Switch between the exact probability P(X = k) and the cumulative probability P(X ≤ k) above the table.

How to use this tool

Choose the number of trials, n, from the buttons.
Switch between the exact probability P(X = k) and the cumulative probability P(X <= k) for the whole table.
Find your value of k down the left side and your success probability p along the top.
The value where they meet is your probability.

Formula Reference

Binomial probability

P(X = k) = C(n, k) p^k (1-p)^(n-k)

Cumulative probability

P(X <= k) = sum from i=0 to k of P(X = i)

ArticleThe Binomial Distribution CalcBinomial Probability Calculator ToolBinomial Distribution Explorer GlossaryGlossary: Binomial Distribution

Frequently Asked Questions

My exact n or p is not in the table. What do I do?+

Use the Binomial Probability Calculator, which computes the exact value for any whole-number n and any probability p, not just the values shown here.

What is the difference between the two views?+

P(X = k) is the probability of exactly k successes. P(X <= k) adds up every outcome from 0 successes through k successes, which is what you need for questions like "at most k" or, by subtraction, "more than k".

How do I find P(X >= k)?+

Switch to the cumulative view, read P(X <= k - 1), and subtract it from 1. Equivalently, 1 minus the cumulative probability up to k - 1 gives the probability of k or more successes.

Why do the probabilities in a row not always decrease as p increases?+

For small k, the probability of exactly k successes typically peaks at some middle value of p and falls off on both sides, since very low or very high success probabilities make a small, specific count of successes less likely.

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.6

0.7

0.75

0.8

0.85

0.9

0.95

0.5987

0.3487

0.1969

0.1074

0.0563

0.0282

0.0135

0.006

0.0025

0.001

0.0001

0.3151

0.3874

0.3474

0.2684

0.1877

0.1211

0.0725

0.0403

0.0207

0.0098

0.0016

0.0001

0.0746

0.1937

0.2759

0.302

0.2816

0.2335

0.1757

0.1209

0.0763

0.0439

0.0106

0.0014

0.0004

0.0001

0.0105

0.0574

0.1298

0.2013

0.2503

0.2668

0.2522

0.215

0.1665

0.1172

0.0425

0.009

0.0031

0.0008

0.0001

0.001

0.0112

0.0401

0.0881

0.146

0.2001

0.2377

0.2508

0.2384

0.2051

0.1115

0.0368

0.0162

0.0055

0.0012

0.0001

0.0015

0.0085

0.0264

0.0584

0.1029

0.1536

0.2007

0.234

0.2461

0.2007

0.1029

0.0584

0.0264

0.0085

0.0015

0.0001

0.0012

0.0055

0.0162

0.0368

0.0689

0.1115

0.1596

0.2051

0.2508

0.2001

0.146

0.0881

0.0401

0.0112

0.001

0.0001

0.0008

0.0031

0.009

0.0212

0.0425

0.0746

0.1172

0.215

0.2668

0.2503

0.2013

0.1298

0.0574

0.0105

0.0001

0.0004

0.0014

0.0043

0.0106

0.0229

0.0439

0.1209

0.2335

0.2816

0.302

0.2759

0.1937

0.0746

0.0001

0.0005

0.0016

0.0042

0.0098

0.0403

0.1211

0.1877

0.2684

0.3474

0.3874

0.3151

0.0001

0.0003

0.001

0.006

0.0282

0.0563

0.1074

0.1969

0.3487

0.5987

Frequently Asked Questions

My exact n or p is not in the table. What do I do?+

Use the Binomial Probability Calculator, which computes the exact value for any whole-number n and any probability p, not just the values shown here.

What is the difference between the two views?+

How do I find P(X >= k)?+

Switch to the cumulative view, read P(X <= k - 1), and subtract it from 1. Equivalently, 1 minus the cumulative probability up to k - 1 gives the probability of k or more successes.

Why do the probabilities in a row not always decrease as p increases?+