binomial probability

简明释义

二项式概率;

英英释义

例句

1.In sports analytics, teams may use binomial probability 二项概率 to evaluate the chances of winning a certain number of games in a season.

在体育分析中，球队可能会使用二项概率 binomial probability 来评估在一个赛季中赢得一定数量比赛的机会。

2.In a game where you flip a coin 10 times, the binomial probability 二项概率 of getting exactly 6 heads can be calculated using the binomial formula.

在一个游戏中，你抛硬币10次，得到恰好6个正面的二项概率 binomial probability 可以通过二项公式计算。

3.A quality control manager uses binomial probability 二项概率 to determine the likelihood of finding defective items in a batch of products.

质量控制经理使用二项概率 binomial probability 来确定在一批产品中发现缺陷物品的可能性。

4.The binomial probability 二项概率 model helps statisticians predict the number of successes in a series of trials.

二项概率 binomial probability 模型帮助统计学家预测一系列试验中的成功次数。

5.When assessing the risk of a new drug, researchers calculate the binomial probability 二项概率 of adverse effects occurring in a sample population.

在评估一种新药的风险时，研究人员计算样本人群中不良反应发生的二项概率 binomial probability。

作文

Understanding the concept of binomial probability is crucial for anyone studying statistics or probability theory. This concept refers to the likelihood of obtaining a fixed number of successes in a specified number of independent trials, where each trial has two possible outcomes: success or failure. The binomial probability formula provides a way to calculate this likelihood. It is expressed as P(X = k) = (n choose k) * p^k * (1-p)^(n-k), where n represents the number of trials, k is the number of successes we are interested in, and p is the probability of success on an individual trial.To illustrate this, let’s consider a simple example involving coin flips. Imagine you flip a fair coin five times. In this scenario, the number of trials (n) is 5, and the probability of getting heads (success) on any single flip (p) is 0.5. If we want to find the probability of getting exactly three heads (k = 3), we can apply the binomial probability formula. First, we calculate the combination of choosing 3 successes out of 5 trials, denoted as "5 choose 3", which equals 10. Next, we calculate the probability of getting heads three times and tails two times, which is (0.5)^3 * (0.5)^2 = 0.5^5 = 0.03125. Finally, multiplying these values together gives us the binomial probability: P(X = 3) = 10 * 0.03125 = 0.3125. Thus, there is a 31.25% chance of flipping exactly three heads in five flips.The binomial probability distribution is not only limited to coin flips; it can be applied in various real-world scenarios. For instance, businesses often use this concept to predict the success rate of marketing campaigns, where they may want to know the probability of achieving a certain number of sales from a specific number of leads. Similarly, in quality control, manufacturers might use binomial probability to determine the likelihood of producing a certain number of defective items in a batch.Moreover, understanding binomial probability is essential for grasping more advanced statistical concepts. It lays the groundwork for the normal distribution, which is widely used in statistics. The Central Limit Theorem states that as the number of trials increases, the distribution of the sample mean will tend to be normally distributed, regardless of the shape of the population distribution. This theorem heavily relies on the principles of binomial probability.In conclusion, the concept of binomial probability is fundamental in the field of statistics. It enables individuals to calculate the likelihood of a specific number of successes in multiple trials, providing valuable insights in various applications, from business to manufacturing. Mastering this concept not only enhances one’s statistical knowledge but also equips individuals with the tools necessary to make informed decisions based on probability. Whether you are a student, a professional, or simply someone interested in understanding the world through data, grasping the principles of binomial probability is an invaluable skill that will serve you well in many areas of life.

理解二项概率的概念对于任何学习统计学或概率论的人来说都至关重要。这个概念指的是在指定数量的独立试验中获得固定数量成功的可能性，其中每次试验有两个可能的结果：成功或失败。二项概率公式提供了一种计算这种可能性的方法。它的表达式为P(X = k) = (n choose k) * p^k * (1-p)^(n-k)，其中n代表试验次数，k是我们感兴趣的成功次数，p是单次试验成功的概率。为了说明这一点，让我们考虑一个简单的例子，涉及抛硬币。想象一下你抛五次公平的硬币。在这种情况下，试验次数(n)为5，每次抛出硬币得到正面(成功)的概率(p)为0.5。如果我们想要找出正好得到三次正面的概率(k = 3)，我们可以应用二项概率公式。首先，我们计算从5次试验中选择3次成功的组合，记作“5 choose 3”，结果为10。接下来，我们计算三次得到正面和两次得到反面的概率，即(0.5)^3 * (0.5)^2 = 0.5^5 = 0.03125。最后，将这些值相乘得到二项概率：P(X = 3) = 10 * 0.03125 = 0.3125。因此，在五次抛掷中正好得到三次正面的概率为31.25%。二项概率分布不仅限于抛硬币；它可以应用于各种现实场景。例如，企业经常使用这个概念来预测营销活动的成功率，他们可能想知道从特定数量的潜在客户中实现一定数量销售的概率。同样，在质量控制中，制造商可能会使用二项概率来确定在一批产品中生产一定数量缺陷品的可能性。此外，理解二项概率对于掌握更高级的统计概念非常重要。它为正态分布奠定了基础，而正态分布在统计学中被广泛使用。中心极限定理指出，随着试验次数的增加，样本均值的分布将趋向于正态分布，无论总体分布的形状如何。这个定理在很大程度上依赖于二项概率的原理。总之，二项概率的概念在统计学领域是基础性的。它使人们能够计算在多次试验中获得特定数量成功的可能性，为各个应用领域提供了宝贵的见解，从商业到制造业。掌握这一概念不仅增强了个人的统计知识，还为个人提供了基于概率做出明智决策所需的工具。无论你是学生、专业人士，还是只是对通过数据理解世界感兴趣的人，掌握二项概率的原则都是一种宝贵的技能，它将在生活的许多领域为你服务。