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A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment and a sequence of outcomes is called a Bernoulli process; for a single trial, i.e., n = 1, the binomial distribution is a Bernoulli distribution. The binomial distribution is the basis for the popular binomial test of statistical significance.

一个单一的结果为成功或失败的实验也被称为<font color="#ff8000">伯努利试验 Bernoulli trial</font>或<font color="#ff8000">伯努利实验 Bernoulli experiment </font>，一系列伯努利实验结果被称为<font color="#ff8000">伯努利过程 Bernoulli process </font>; 对于一个单一的实验，即''n''&nbsp;=&nbsp;1，这个二项分布是一个<font color="#ff8000">伯努利分布 Bernoulli distribution</font>。二项分布是流行<font color="#ff8000">统计显著性 statistical significance </font><font color="#ff8000">二项检验 binomial test </font>的基础。

一个单一的结果为成功或失败的实验也被称为<font color="#ff8000">伯努利试验 Bernoulli trial</font>或<font color="#ff8000">伯努利实验 Bernoulli experiment </font>，一系列伯努利实验结果被称为<font color="#ff8000">伯努利过程 Bernoulli process </font>; 对于一个单一的实验，即''n''&nbsp;=&nbsp;1，这个二项分布是一个<font color="#ff8000">伯努利分布 Bernoulli distribution</font>。二项分布是<font color="#ff8000">统计显著性 statistical significance </font>的<font color="#ff8000">二项检验 binomial test </font>的基础。

is the binomial coefficient, hence the name of the distribution. The formula can be understood as follows. k successes occur with probability pk and n&nbsp;−&nbsp;k failures occur with probability (1&nbsp;−&nbsp;p)n&nbsp;−&nbsp;k. However, the k successes can occur anywhere among the n trials, and there are  \binom{n}{k} different ways of distributing k successes in a sequence of n trials.

is the binomial coefficient, hence the name of the distribution. The formula can be understood as follows. k successes occur with probability pk and n&nbsp;−&nbsp;k failures occur with probability (1&nbsp;−&nbsp;p)n&nbsp;−&nbsp;k. However, the k successes can occur anywhere among the n trials, and there are  \binom{n}{k} different ways of distributing k successes in a sequence of n trials.

是<font color="#ff8000">二项式系数</font>，因此有了分布的名字。这个公式可以理解为，K次成功发生在概率为''p''^''k''的情况下，''n''&nbsp;−&nbsp;''k''次失败发生在概率为(1&nbsp;−&nbsp;''p'')^{''n''&nbsp;−&nbsp;''k''}的情况下。然而，''k''次成功可以发生在''n''个试验中的任何一个，并且在''n''个试验序列中有<math>\binom{n}{k}</math>种''k''次试验成功的不同分配方法。

是<font color="#ff8000">二项式系数 binomial coefficient</font>，因此有了分布的名字。这个公式可以理解为，K次成功发生在概率为''p''^''k''的情况下，''n''&nbsp;−&nbsp;''k''次失败发生在概率为(1&nbsp;−&nbsp;''p'')^{''n''&nbsp;−&nbsp;''k''}的情况下。然而，''k''次成功可以发生在''n''个试验中的任何一个，并且在''n''个试验序列中有<math>\binom{n}{k}</math>种''k''次试验成功的不同分配方法。