Random phenomena exist in all aspects of our daily life and in all fields of science and technology. Probability theory is a science that guides people to see the essence of things from their appearances. This paper discusses the wide application of probability knowledge from some phenomena in real life.
Keywords: random phenomenon; Probability; applied analysis
In nature and real life, some things are interrelated and constantly developing. In their relationship and development, they can be divided into two categories according to whether there is an inevitable causal relationship: one is deterministic phenomenon, which means that under certain conditions, it will definitely lead to certain results. For example, if water is heated to 100 degrees Celsius at standard atmospheric pressure, it will inevitably boil. This connection between things is inevitable. The other is uncertainty. The result of this phenomenon is uncertain under certain conditions. For example, if the same worker processes several similar parts on the same machine tool, there will always be a little difference in size. For another example, under the same conditions, the artificial germination test of wheat varieties, the germination of each seed is not the same, such as strength, morning and evening differences and so on. Why is there such an uncertain result in the same situation? This is because when we say "equal conditions", we mean some major conditions. In addition to these main conditions, there will be many secondary conditions and accidental factors that people cannot predict in advance. This phenomenon, we can not use the inevitable causal relationship to make a clear answer to the result of the phenomenon in advance. This relationship between things is accidental, and this phenomenon is called accidental phenomenon or random phenomenon.
Probability is simply the probability of one thing happening. For example, the sun rises and sets every day, and the probability of this happening is 100% or 1, because it will definitely happen; The probability that the sun rises in the west and sets in the east is zero, because it will definitely not happen. But many phenomena in life may or may not happen, such as whether it will rain one day, buying defective products and so on. The probability of such an event is between 0 and 100%, or between 0 and 1. In daily life, no matter whether the stock market rises or falls or some accident happens, any unpredictable event that needs to be explained by "luck" can be quantitatively analyzed by probability model. Uncertainty not only brings people a lot of trouble, but also is often an effective or even the only means to solve problems.
Walking on the street, the coming and going vehicles are reminiscent of probability; Production and life are inseparable from probability. In the exciting lottery, probability also guides our practice. After the stock market, lottery has become a hot spot in the economic life of urban and rural residents. According to statistics, there are 3 lottery players in China 100. According to the survey results of residents in Beijing, Shanghai and Guangzhou, 50% of them have bought lottery tickets, and 5% have become "professional" (economic purchase) lottery players. The dream of "making a small fortune" is the same mentality of many lottery players. So, can buying lottery tickets really make us get what we want? Take 7 out of 36 numbers as an example. It seems that it is not difficult, but it is actually "out of reach". After calculation, the theoretical winning probability of one bet is as follows:
It can be seen that only a few people can win the prize, and buyers should have a normal mind, which can neither be used as a pure investment nor as a way to get rich.
In sports competitions, one game decides the outcome. Although both sides have a 50-50 chance of winning, there are too few games and the commercial value is not great. Therefore, the organizers generally adopt the method of "two wins in three games" or "three wins in five games" to decide the outcome, which not only satisfies the contestants, but also can be accepted by the audience, and the organizers make rich profits. So is it really fair to both players? Let's explain it with the viewpoint and knowledge of probability: in our daily life, we always hope that our luck will be better, and there are many people who try their luck, just like candidates are facing an exam. Of course, there are real scholars, but there are also many people who are lucky enough to make up the numbers. So, can you pass the formal exam by luck alone? Let's take Band 4 as an example to illustrate this problem.
CET-4 is a comprehensive test of college students' English proficiency, which has certain difficulties, including listening, grammatical structure, reading comprehension, filling in the blanks, writing and so on. Except writing 15, the other 85 questions are multiple-choice questions, and each question has four options, A, B, C and D. This situation makes individual students feel very lucky, so can they pass Band 4 by luck? The answer is no, assuming that the writing score of 15 is not considered, 85 questions must be answered correctly if the passing score is above 60,51,which can be regarded as an 85-fold Bernoulli test.
The probability is very small, which is equivalent to that only 0.874 of the 65.438+000 billion lucky candidates can pass. So it is impossible to pass the exam by luck.
Therefore, in our life and work, no matter what we do, we should be down-to-earth and rationally analyze and treat some accidents in life. A philosopher once said, "Probability is the real guide of life". With the development of production and the progress of science and technology, probability has penetrated into all fields of our lives. As we all know, insurance, post and telecommunications systems make full use of probability knowledge in the profit calculation of issuing prize postcards, the prediction of admission scores, and even the estimation of prisoners' height by the length of footprints.
Nowadays, "precipitation probability" has been impressive on TV and newspapers. Some people imagine that in the near future, every news item in the news report will be marked with "true probability" and every program in the TV program preview will be written with "visible probability". In addition, there are watermelon maturity probability, train punctuality probability, prescription efficacy probability, advertising reliability probability and so on. Because probability is the expression of equal possibility, in a sense, it is the embodiment of democracy and equality, so many competition mechanisms in social life can be explained by probability.
In short, due to the existence of a large number of random phenomena in the real world, probability will inevitably show its great power more and more.
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