Most people have studied probability in middle school, but mastering the calculation method of probability does not mean that they really understand probability. In fact, there are several key ideas in probability theory that most math teachers simply don't understand or even talk about. You don't even need to do any calculations to understand these ideas, but they can fundamentally change our view of the world.
1. Whatever
The most basic idea of probability theory is that some things happen for no reason. There can be no causal relationship between the occurrence of some things and anything that happened before. Whatever you do, you can't let it happen, and you can't let it not happen.
Buy lottery tickets: For a person who has never bought a lottery ticket, it is entirely possible and equally possible to take the highest prize in a certain lottery. Winning the prize is not the result of his own efforts, nor is it "God's care" for him; One miss doesn't mean someone is targeting him. This is "randomness", and you can't control the result anyway. Easy to understand, right?
Most things are not completely random events, but there are some random factors. If contingency and inevitability are combined, it is not so easy to understand. People often misunderstand accidents and always want to explain them by necessity.
So for smart people, accidental factors are not worth taking seriously. By understanding randomness, we know that some things happen as soon as they happen, which is of little significance for interpretation. We can learn nothing from this matter, which is not worth taking seriously or even taking action at all.
In reality, a few successful people have legendary experiences and stories, which are all accidental factors that have been beautified.
Step 2 be wrong
Most things contain both accidental and inevitable factors. Accidental failures and achievements are not worth making a fuss about. Can it be judged according to inevitable factors? Yes, but you must understand the mistakes. Anything that has no absolute value has a certain error, and even the error may be a range. The error we usually see only means that there are more possibilities and times in this range.
With the concept of error, we should learn to ignore any fluctuation within the error range. The same is true of exam results. Suppose a classmate passed CET-4 twice, with 57 points for the first time and 63 points for the second time. He said it was a small step forward. I said it's not progress, but it's all within the measurement error range.
3. Gambler fallacy
There is indeed a "law of large numbers" in probability theory, which says that if there are enough lucky draws, the frequency of different results is equal to their probability. But people often misunderstand randomness and the law of large numbers-thinking that randomness is uniformity. If what happened in the past is not so unified, people will mistakenly think that things in the future will try to "smooth out".
Two jokes:
For example, there is a joke that a person always carries a bomb when flying. He thinks that no terrorists will blow up the plane-because the possibility of two bombs on a plane should be very small!
For example, soldiers on the battlefield have a saying that if a bomb explodes beside you in battle, you should jump into the crater quickly-because it is unlikely that two bombs will hit the same place. This is all caused by ignorance of independent random events.
4. Find the law where there is no law.
Knowing randomness and independent random events, we can draw a conclusion that the occurrence of independent random events is irregular and unpredictable. This is a very important wisdom.
It is quite easy to find a rule in an irregular place, as long as you are willing to ignore all the data that do not conform to your rules. 9 and 15 are not prime numbers, that's an accident. The law found in the case of small data only summarizes the existing experience.
If there is enough data, we can find any pattern we want. It's like biblical code. Some people regard the Bible as a string game, looking for letter combinations that can correspond to world events in a specific position, and claim that this is a prophecy of the Bible for future generations. The problem is that these "predictions" can perfectly explain what has happened, and when you predict what has not happened, you won't get such a good result. In the case of sufficient data, the summary law is only a verification of the limited life.
5. Decimal law
If there is enough data, some "rules" will jump out on their own, and you can't even believe it. With less data, random phenomena can look "not random" or even neat, and feel really regular.
The law of large numbers says that if the statistical sample is large enough, the frequency of things can be infinitely close to its theoretical probability-that is, its "nature". The law of decimals says that if the sample is not large enough, it will show all kinds of extreme situations, which may have nothing to do with nature.
It is possible to draw completely wrong conclusions by using the law of decimals.
Here is only a very objective description of the importance of probabilistic thinking in modern society, using probabilistic thinking to understand life. There will be a lot of relief after reading it. The lottery theory and gambler's fallacy mentioned in the book have all happened before. I used to know some knowledge of probability, but having knowledge doesn't mean I can use it. It may not be thorough enough. Today is thorough, but I feel relaxed.