1. Random events refer to events that may or may not occur under certain conditions. In other words, a random event refers to an event with uncertainty under certain conditions. Random events can be divided into deterministic random events and uncertain random events. The probability of deterministic random events is 1, that is, it will definitely happen; The probability of an uncertain random event is between 0 and 1, which means it may or may not happen. The set of random events is called sample space, which is usually represented by the capital letter S.
2. Sample space refers to the collection of all possible results in the experiment. In probability theory, we usually care about the size of the sample space, that is, the number of possible results of the experiment. For example, in the dice roll experiment, the probability of each face-up is main 1/6, so the size of the sample space is 6, which can be represented by the capital letter n, that is, N = {1, 2, 3, 4, 5, 6}. Sample space can also be represented by more specific symbols, such as the numbers 1, 2, 3, 4, 5 and 6, which represent all possible results when rolling dice.
3. Probability is a numerical value used to measure the possibility of random events. In probability theory, probability is usually expressed by P(A), where A is a random event. The probability ranges from 0 to 1, where 0 means that the event cannot happen and 1 means that the event will happen. The calculation method of probability is usually determined by experiment or observation. For example, the probability of throwing a coin upside down can be calculated through many experiments, and the probability of upside down is about 0.5.
4. Conditional probability refers to the possibility of an event under given conditions. In other words, conditional probability is the probability that one event will happen when it is known that another event will happen. Conditional probability can be represented by P(B|A), where a is a random event, b is another random event, and P(A) represents the probability of occurrence of event A. For example, in the dice experiment, it is known that the probability of throwing 1 point is 1/6, and now it is required to throw 2 points.
Concepts other than the four basic concepts of probability theory
In addition to the four basic concepts of probability theory, probability theory has many other concepts, such as conditional probability, independence, random variables, random processes and so on. A deep understanding of these concepts is very important for understanding the basic principles of probability theory and solving practical problems. Therefore, learning probability theory not only needs to master its basic concepts, but also needs to deeply understand these concepts through practice and theoretical study, and can be applied to practical problems.