Probability Thought in Ancient Proverbs of China

In ancient mathematics in China, there were applications of probability, such as setting leap and divination. But there is no systematic probability theory, and there is no complete probability theory thought.

The basic concept of probability is a quantitative index indicating the possibility of a certain situation (event), which is between 0 and 1.

If the probability of an event is close to zero, it means that it is almost impossible to happen. If the probability of an event is close to 1, it indicates that the event is almost certain to happen.

Subjective probability:

Subjective probability can be understood as a state of mind or tendency based on the subjective estimation of the possibility of an event based on experience and knowledge.

The event here is defined as a random event, the so-called "random event", that is, the result is accidental.

Classical probability:

The classic definition is that it can only be used when all the test results are limited and the possibility is established. In some cases, this concept can be extended to the case of infinite test results.

The core of classical probability is actually "counting". First, the number of basic events in the sample space is $N$, and then the number of basic events contained in event $A$ is $M$.

Geometric probability:

The basic idea of geometric probability is to correspond an event to a geometric region and calculate the probability of an event by using the measurement of the geometric region.

Frequency definition of probability;

1. The random phenomenon related to the investigation event A can be repeated a lot.

2. In the $n$ repetition test, let $n(A)$ be the frequency of event $A$, also called $n(A)$ be the frequency of event $A$. Let $f_n(A)=frac{n(A)}{n}$ be the frequency of event $A$.

3. Long-term practice shows that the frequency $f_n(A)$ will stabilize around a certain constant $a$ with the increase of experimental repetition $n$, which is called the stable value of frequency. The stable value of this frequency is the probability we seek.