Statistics 简明教程

Statistics - Probability

Probability

概率意味着“可能性”或“机会”。如果一个事件肯定会发生，则该事件发生的概率为 1，如果肯定不会发生，则该事件发生的概率为 0。

Probability implies 'likelihood' or 'chance'. When an event is certain to happen then the probability of occurrence of that event is 1 and when it is certain that the event cannot happen then the probability of that event is 0.

因此，概率的值范围是 0 到 1。概率已被各个思想流派以不同的方式定义。以下讨论其中一些。

Hence the value of probability ranges from 0 to 1. Probability has been defined in a varied manner by various schools of thought. Some of which are discussed below.

Classical Definition of Probability

顾名思义，古典概率定义方法是最古老的方法。它指出，如果有 n 个穷举的、互斥的和同样可能的案例，其中 m 个案例有利于事件 A 的发生，

As the name suggests the classical approach to defining probability is the oldest approach. It states that if there are n exhaustive, mutually exclusive andequally likely cases out of which m cases are favourable to the happening ofevent A,

然后事件 A 的概率由以下概率函数定义：

Then the probabilities of event A is defined as given by the following probability function:

Formula

因此，为了计算概率，我们需要有关有利情况数和完全可能情况总数的信息。可以使用以下示例对其进行解释。

Thus to calculate the probability we need information on number of favorable cases and total number of equally likely cases. This can he explained using following example.

Example

Problem Statement:

Problem Statement:

抛硬币。正面朝上的概率是多少？

A coin is tossed. What is the probability of getting a head?

Solution:

Solution:

完全可能的结果总数 (n) = 2（即正面或反面）

Total number of equally likely outcomes (n) = 2 (i.e. head or tail)

有利于正面的结果数 (m) = 1

Number of outcomes favorable to head (m) = 1