compound probability

简明释义

合成概率

英英释义

例句

1.To find the chance of rolling a 3 or a 4 on two dice, we use compound probability (复合概率) to calculate the total outcomes.

要找出在两个骰子上掷出3或4的机会，我们使用复合概率来计算总结果。

2.When calculating the compound probability (复合概率) of independent events, you multiply their individual probabilities.

在计算独立事件的复合概率时，你需要将它们各自的概率相乘。

3.The compound probability (复合概率) of flipping heads on two coins is 1/4.

抛两枚硬币得到正面的复合概率是1/4。

4.In a card game, the compound probability (复合概率) of drawing an Ace and then a King can be calculated by multiplying the individual probabilities.

在一场纸牌游戏中，抽到一张Ace然后再抽到一张King的复合概率可以通过相乘各自的概率来计算。

5.The compound probability (复合概率) of getting a red ball from one box and a blue ball from another is found by multiplying the probabilities from each box.

从一个箱子里拿到一个红球和从另一个箱子里拿到一个蓝球的复合概率是通过将每个箱子的概率相乘来找到的。

作文

In the world of mathematics, probability plays a crucial role in understanding uncertainty and making informed decisions. One of the key concepts within probability is compound probability, which refers to the likelihood of two or more independent events occurring simultaneously. Understanding compound probability is essential for various fields, including statistics, finance, and science, as it helps individuals assess risks and make predictions based on multiple factors. To grasp the concept of compound probability, it is important to first understand the basic principles of probability. Probability is a measure of how likely an event is to occur, expressed as a number between 0 and 1. A probability of 0 means that the event will not happen, while a probability of 1 indicates certainty that the event will occur. When we deal with multiple events, we often need to calculate the combined probability of these events happening together, which leads us to compound probability. There are two primary types of compound probability: independent events and dependent events. Independent events are those where the occurrence of one event does not affect the occurrence of another. For example, flipping a coin and rolling a dice are independent events. The probability of both events happening can be calculated by multiplying their individual probabilities. If the probability of getting heads when flipping a coin is 1/2, and the probability of rolling a three on a die is 1/6, the compound probability of both events occurring is (1/2) * (1/6) = 1/12.On the other hand, dependent events are those where the outcome of one event influences the outcome of another. For instance, if you draw a card from a deck and do not replace it, the probability of drawing a second card is affected by the first draw. In this case, to find the compound probability, you must consider how the first event changes the total number of possible outcomes for the second event. If the first card drawn is a heart, there are now only 12 hearts left in a deck of 51 cards. Thus, the compound probability of drawing two hearts consecutively would involve calculating the probability of the first draw and then adjusting the probability for the second draw accordingly.Understanding compound probability is not just an academic exercise; it has real-world applications. For example, in the field of finance, investors often need to assess the risk of multiple investments simultaneously. By understanding the compound probability of various market conditions, they can make more informed decisions about where to allocate their resources. Similarly, in healthcare, researchers may study the compound probability of different risk factors contributing to a disease, helping to identify effective prevention strategies.In conclusion, compound probability is a fundamental concept in probability theory that allows us to evaluate the likelihood of multiple events occurring together. By understanding both independent and dependent events, we can apply this knowledge in various fields, enhancing our decision-making processes and improving our ability to navigate uncertainty. Mastering compound probability empowers individuals to analyze complex situations and make predictions based on a combination of factors, ultimately leading to better outcomes in both personal and professional endeavors.

在数学的世界中，概率在理解不确定性和做出明智决策方面发挥着关键作用。其中一个关键概念是复合概率，它指的是两个或多个独立事件同时发生的可能性。理解复合概率对于统计学、金融和科学等多个领域至关重要，因为它帮助人们评估风险并根据多个因素做出预测。要掌握复合概率的概念，首先需要理解概率的基本原则。概率是衡量事件发生可能性的一个指标，通常用0到1之间的数字表示。概率为0意味着事件不会发生，而概率为1则表示事件一定会发生。当我们处理多个事件时，通常需要计算这些事件同时发生的联合概率，这就引出了复合概率。复合概率主要有两种类型：独立事件和依赖事件。独立事件是指一个事件的发生不影响另一个事件的发生。例如，抛硬币和掷骰子是独立事件。这两个事件同时发生的概率可以通过将它们各自的概率相乘来计算。如果抛硬币得到正面的概率是1/2，而掷骰子得到三的概率是1/6，那么这两个事件同时发生的复合概率为(1/2) * (1/6) = 1/12。另一方面，依赖事件是指一个事件的结果影响另一个事件的结果。例如，如果你从一副牌中抽出一张牌而不放回，那么第二张牌的概率就会受到第一次抽取的影响。在这种情况下，要找到复合概率，必须考虑第一次事件如何改变第二次事件的可能结果总数。如果第一次抽到的是红心，那么在51张牌中只剩下12张红心。因此，连续抽到两张红心的复合概率需要计算第一次抽取的概率，然后相应地调整第二次抽取的概率。理解复合概率不仅仅是学术练习，它具有现实世界的应用。例如，在金融领域，投资者常常需要评估多个投资的风险。通过理解各种市场条件的复合概率，他们可以做出更明智的资源配置决策。同样，在医疗保健领域，研究人员可能会研究不同风险因素对某种疾病的复合概率，帮助识别有效的预防策略。总之，复合概率是概率论中的一个基本概念，使我们能够评估多个事件同时发生的可能性。通过理解独立事件和依赖事件，我们可以将这一知识应用于多个领域，增强我们的决策过程，提高我们应对不确定性的能力。掌握复合概率使个人能够分析复杂情况，并根据多种因素做出预测，从而最终在个人和职业努力中获得更好的结果。