What is the use of learning probability theory?

Probability theory permeates every aspect of modern life. As Laplace, the famous 19th-century French mathematician, said: "For most of life, the most important questions are really just questions of probability. You could say that almost all the knowledge we have is uncertain, and there is only one A small part of what we know with certainty. Even the mathematical sciences themselves, induction, analogy, and the first means of discovering truth are based on the theory of probability. The entire system of human knowledge is therefore tied to this theory... …”

The following are some cases from history.

The ratio of male to female babies at birth

Most people may think that the possibility of giving birth to a boy or a girl is equal, so they speculate that the ratio of the number of male babies to female babies should be 1 :1, but this is not the case.

In 1814 AD, the French mathematician Laplace (1794-1827) recorded some interesting statistics in his new book "Philosophical Discussion of Probability". Based on statistics from London, Petersburg, Berlin and all of France, he concluded that the ratio of the number of male babies to female babies was almost exactly 22:21. That is, among all babies born, boys accounted for 51.2%, and girls accounted for 51.2%. Infants account for 48.8%. But strangely, when he calculated the birth rate of boys in Paris for the entire 40 years from 1745 to 1784, he got another ratio of 25:24, with boys accounting for 51.02%, a difference of 0.14% from the former. Laplace was puzzled by this tiny difference of one thousandth and four thousandths. He firmly believed in the laws of nature. He felt that there must be profound factors behind this one and four thousandths. So, he conducted in-depth investigation and research, and finally discovered that at that time, Parisians "valued girls over boys" and had the bad custom of abandoning male babies, which distorted the truth about the birth rate. After correction, the birth ratio of male to female babies in Paris was still 22: twenty one.

An excellent mathematician = 10 divisions

In World War II, the United States once announced that the role of an excellent mathematician is more than the strength of 10 divisions. This sentence has an unusual origin.

Before 1943, the British and American transport fleets in the Atlantic were often attacked by German submarines. At that time,

Britain and the United States were limited by their strength and were unable to send more escort ships. At that time, the German "submarine warfare" caused the Allies to be in dire straits.

For this reason, a U.S. Navy general consulted several mathematicians. The mathematicians used probability theory to analyze and analyze that the encounter between the fleet and the enemy submarine was a random event. From a mathematical point of view, this A question, it has certain regularity. The smaller the formation size of a certain number of ships (100 ships), the more formations there are (for 20 ships each time, there will be 5 formations). The more formations, the greater the probability of encountering the enemy. The U.S. Navy accepted the mathematician's suggestion and ordered the fleet to assemble in designated sea areas, then collectively pass through dangerous sea areas, and then each sail to the predetermined port. As a result, a miracle occurred: the probability of the Allied fleet being attacked and sunk was reduced from 25% to 1%, greatly reducing losses and ensuring the timely supply of supplies.

What is probabilistic weather forecast?

Probabilistic weather forecast uses probability values ??to express the likelihood of the forecast quantity occurring. What it provides is not the "prevalence" of a certain weather phenomenon. Or "none", the "big" or "small" value of a certain meteorological element, but the likelihood of the weather phenomenon occurring. For example, when it comes to precipitation forecasts, traditional weather forecasts generally predict rain or no rain, while probabilistic forecasts give a percentage of possible precipitation. The greater the percentage, the greater the possibility of precipitation. Generally speaking, if the probability value is less than or equal to 30%, it can be considered that there will be basically no precipitation; if the probability value is 30%-60%, precipitation may occur, but the possibility is small; if the probability value is 60%-70%, precipitation is very likely Large; the probability value is greater than 70%, and precipitation will occur. Probabilistic weather forecast reflects not only the deterministic aspect of weather changes, but also the uncertainty and degree of uncertainty of weather changes. In many cases, this form of forecast is more suitable for decision-making needs in economic and military activities.

What is the probability of HIV infection?

What is the probability of HIV infection? According to Xu Keyi, Director of the Sexually Transmitted Disease Prevention and Control Center of Ditan Hospital, AIDS is transmitted to others through three transmission routes, namely: blood transmission, sexual transmission, and mother-to-child transmission. If a normal person is transfused with the blood of an HIV (AIDS virus) positive person or an AIDS patient, the probability of infection is 95%, and the probability of infection when an HIV positive person or an already sick patient has sexual intercourse with a normal person is 95%. Gender has a certain relationship. The probability of male-to-female transmission is 0.2%, and the probability of female-to-male transmission is 0.1%. The probability of male-to-male transmission is much greater than the above two methods. If the mother is an HIV-positive or AIDS patient, the probability of infection to the fetus is 25%, but if the mother undergoes antiviral treatment with AZT, the probability of infection of the fetus drops to 8%; after combined therapy (cocktail therapy) treatment of the fetus The probability of infection may drop to 2%.

HIV is a very fragile virus that is very sensitive to heat and dryness. HIV dies in 10 minutes in a dry environment and is inactivated in 30 minutes at 60 degrees Celsius.

If a syringe that has just come into contact with blood on a patient's body is immediately inserted into a normal human body, the probability of infection is less than 0.3%. This is why mosquito bites do not transmit AIDS.

It is being carried out intensively, such as the AIDS vaccine developed using traditional medical methods; the AIDS antibody developed using traditional Chinese medicine technology; and the use of "condoms" promoted from the perspective of family planning. These all allow us to see To the dawn of mankind overcoming AIDS.

Do you know the probability of winning the lottery?

The probability of "choose 7 from 36" and "choose 5 from 26"

According to relevant experts, the sports lottery currently issued in Guangdong Province " "36 Pick 7", Nan Yue Style "36 Pick 7", and Nan Yue Style "26 Pick 5" are all digital combination games, and the winning probability is calculated in the same way. The jackpot hit probability of the "36 Pick 7" game is 1/8347680, the probability of winning the first prize in the "26 Pick 5" gameplay is 1/65780; the current sports lottery "36 Pick 7" secondary lottery winning probability is still 1/8347680, and the Southern Guangdong style "36 Pick 7" provincial special award The probability of winning the prize (win 8 numbers) is 1/32060340, the probability of winning the Southern Guangdong Style "Choose 7 out of 36" Lucky Star Award (win 9 numbers) is 1/94143280, the probability of winning the Southern Cantonese Style "Choose 5 out of 26" lucky prize (win 7 number) is 1/657800.

Smoking is life-threatening: 50% quitting smoking equals self-help

In November 1987, the World Health Organization (WHO) held the 6th International Conference on Smoking and Health in Tokyo, Japan. It is recommended that April 7, 1988, the 40th anniversary of the founding of the World Health Organization, be designated as "World No Tobacco Day" and the slogan "Smoking or health" be put forward. In 1989, the World Health Organization changed this day to May 31 every year.

On May 31 this year, we will usher in the 17th World No Tobacco Day, but the current smoking situation in our country is not optimistic: the number of smokers continues to increase, reaching 320 million, and the average age of smokers is The number of female smokers and teenagers smoking is increasing.

Everyone has played lottery. This game is very interesting, and it is also considered by everyone to be the fairest way to choose. Isn’t probability also used in it? Coins are also a form of drawing lots, it's just a matter of choosing one of the two with different probabilities. The design of many games is either purely based on probability, or uses probability to deceive people. If you really want to play, of course you have to see the essence of things, otherwise it would be silly.

The things mentioned above may be easier for everyone to understand, but there are some probabilities that everyone cannot draw a more precise conclusion, and therefore many people are confused about this. For example, for a person who yearns for love, if asked: What do you think is the probability of meeting your ideal partner? How many people can answer. Of course, we can say that God has another for everyone, but this is a matter of probability, not 100%. Also, how likely does each person think he or she will become rich in the future? This question probably has a variety of strange answers. Some people say it’s not possible, is that true? Rationally speaking, anyone has the possibility of development, except he is a dead person. I mentioned the issue of blind date in my previous blog. Here we also take a look at its probability issue.