Combined Events | 组合事件

📚 Combined Events | 组合事件

In probability, most real-life situations involve more than one event happening together. When we consider two or more events at the same time, such as rolling a die and tossing a coin, we are working with combined events. These situations require careful organisation of outcomes and the correct application of rules for AND and OR combinations.

在概率论中，大多数现实生活场景都涉及多个事件同时发生。当我们同时考虑两个或更多事件时——例如掷骰子和抛硬币——我们就是在处理组合事件。这类情形需要我们仔细整理所有结果，并正确运用”且”与”或”的组合法则。

1. Sample Space Diagrams | 样本空间图

A sample space diagram is a table that lists every possible outcome when two events occur together. For two independent events with m and n outcomes respectively, the total number of combined outcomes is m × n. This is often called the fundamental counting principle.

样本空间图是一个表格，列出两个事件同时发生时的所有可能结果。对于分别有 m 种和 n 种结果的两个独立事件，组合结果总数为 m × n。这通常被称为基本计数原理。

For example, when rolling two fair six-sided dice, each die has 6 outcomes, so the sample space has 6 × 6 = 36 equally likely outcomes. The table below shows every possible sum of the two dice.

例如，掷两个公平的六面骰子时，每个骰子有 6 种结果，因此样本空间共有 6 × 6 = 36 种等可能的结果。下表显示了两个骰子点数之和的所有可能情况。