Wen | Chu Xi
I don't know if you have this impression, when you do test questions in school, when you encounter questions that will not be, there will be some "well-meaning people" to remind you that choosing C is right, because the probability of C choosing the right option is relatively high?
Although the intellectual side will feel a little unreliable, it is undeniable that when encountering a topic that really does not, it will be subconsciously affected by this statement and choose C.
But then, I heard some different claims that the probability of the B option being correct was the highest.
So, the question is, which statement is true? Or are these claims really plausible?
The author of Liu Jia's recently read "Liu Jia's General Lecture Notes on Probability Theory", Liu Jia is an associate professor at Nanjing University, teaching and research direction is probability and mathematical statistics, and is committed to teaching abstract mathematical concepts, tools and methods in an easy-to-understand way.
This book was born out of Liu Jia's general education course "22 Lectures on Probability Theory" on the App, aiming to take the common phenomena in life as the starting point, from the perspective of general education, introduce normal distribution, power law distribution, law of large numbers, Bayesian calculation, variance and expectation and other probability-related knowledge, reawaken the reader's probability awareness, cultivate probability thinking, in order to better think, judge and make choices.
The book has seven chapters, first introducing the nature of probability theory and its four cornerstones - randomness, probability, independence and probability measurement, so that readers can glimpse the foundation of probability theory in the shortest possible time, and then through a series of interesting and vivid cases, in the process of learning how to calculate probability, gradually develop probability thinking.
Inside pages of the book
<h1 class="pgc-h-center-line" data-track="21" >, random is unpredictable</h1>
The essence of probability theory in solving random problems is to transform local randomness into overall certainty.
Well, the concept of "random" is involved here. Interestingly, mathematicians have been arguing for so many years and have not been able to come up with a uniform definition of the word "random." "The only consensus they can reach is that random is unpredictable," Liu Jia explains in the book.
However, unpredictable randomness does not equal uncertainty.
Instead, randomness refers to all the possible outcomes of an event that we all know, but we don't know which outcome will be the next occurrence. For the simplest example, we will have a random play option when listening to music, but I don't know if you have noticed that the premise of random play must also be - in the established song list, random play.
Net map, invasion and deletion
Uncertainty, on the other hand, means that we have no idea what other outcomes of an event might occur. For example, the "black swan event" refers to unpredictable unexpected events. Because it is uncertain, it is impossible to predict, and naturally it cannot be described by probability.
However, the opposite "grey rhino incident", the gray rhinoceros that is close at hand, is bulky and slow to react, and we often ignore its danger, but once it rushes towards us, it will catch people off guard.
Risks like this that are ignored because they are too common, that is, foreseeable potential risks, but do not know when they will occur, this randomness belongs to the study of probability theory.
Essentially, uncertainty encompasses randomness, which is a type of uncertainty. When we encounter uncertainty problems, we can try to turn them into randomness problems, so that we can use the method of probability to study.
<h1 class="pgc-h-center-line" data-track="117" > the nature of probability theory</h1>
Let's look at one of the most famous thought experiments in quantum mechanics, Schrödinger's cat, in a closed box, with a live cat and a bottle of poison. Then there is a radioactive device in the box, and the radioactive material inside may or may not decay within 1 hour.
If the radioactive material decays, it will trigger the device, smash the poison bottle, and the cat will be poisoned; naturally, if the radioactive material does not decay, the cat will still live well.
Well, that's interesting! Until we opened the box, we couldn't be sure if the cat inside was dead or alive.
According to quantum mechanics, the cat in the box is in a "superposition of life and death", that is, the cat is both dead and alive. If you want to determine the answer, only by opening the box and the superposition state is over can you finally determine the state of the cat - dead or alive.
Although before this, we were not sure whether the cat in the box would die or live in the next second, the superposition of its probability of life and death was determined, that is, there was a 50% probability.
And this is the essence of probability theory, not to help you predict what will happen in the next second, but to portray the overall certainty of the world for you.
With this thinking, we can make mathematically deterministic judgments about some random events in life, and even random events that may appear in the future.
<h1 class="pgc-h-center-line" data-track="119" > three, true random, pseudo random, and effect random</h1>
Interestingly, randomness is also divided into three cases: true random, pseudo-random, and effect random.
Going back to the multiple choice question at the beginning of this article, if it is absolutely unpredictable "true randomness" in mathematical logic, then the probability of correctness in each of the four ABCD options is the same.
The reason why there is a legend that an option is more correct is because of the phenomenon of "pseudo-random", that is, an event that appears to be random, but it is not.
Pseudo-random phenomena can improve the correct probability by looking for the laws of events.
I remember that Mr. He Fan once shared how to use big data and statistical laws to improve prediction ability in his "Big Picture" course. He summarized seven exam secrets, including several related to multiple choice questions:
1, of the four-choice multiple-choice questions, the probability that B is the correct answer is 28%; the probability that E is the correct answer is 23% for the five options; and I have always been believed that the C option is only 17% of the probability of the correct answer... (So, the person who told me this law back then, isn't it...?) ）
2, the answer options have "all of the above are right" and "all of the above are wrong", choose these two; the probability of these two options being the correct answer is as high as 52%.
3, the probability that the longest option in the multiple choice question is the correct answer is also the greatest, because the author must ensure that the correct answer is indisputable, so it will be as standardized and complete as possible.
……
Frankly speaking, I was suspicious when I read Mr. He Fan's article before, but when I read "Liu Jia's General Lecture Notes on Probability Theory" and learned that there is also a "pseudo-random" phenomenon in the randomness of probability, I can be considered to have completely understood the mystery.
As Teacher Liu Jia gave another example in the book - when he and his daughter played with rock scissors cloth, he soon discovered his daughter's punching rules, and after each stone, he would make a cloth... Naturally, Teacher Liu Jia, who discovered this law, can basically control the outcome of the game
Therefore, as long as a law can be found in an event, then the event is not true random, but pseudo-random.
So, what does it mean that the effect is random?
Continuing to take Liu Jia's daughter as an example, if she plays this game with another child who can't see the rules, then this punch is no longer pseudo-random, but the effect is random. That is to say, when the effect perceived by children is random, it can be treated as random.
In short, when we talk about the randomness of probability, the "true randomness" in the absolute sense only exists at the quantum level, which is difficult to encounter in reality; those random events that can be found are just "pseudo-randoms" cloaked in randomness; most of the random phenomena in real life are actually effect random, and these are the objects that the discipline of probability theory should focus on.
<h1 class="pgc-h-center-line" data-track="121" >4, written at the end of the article:</h1>
Harari, the author of A Brief History of the Future, once said, "For the future world, the greatest constant is change."
Since change is already the norm in this world, is it possible to use probabilistic thinking to make more rational choices in an uncertain future?
The answer is clearly yes. At the end of this book, Teacher Liu Jia also summarized the three major cultivation principles of probabilistic thinking for us, namely:
1) Confrontation with intuition, can be calculated;
2) Look for conditions and increase the probability;
3) Believe in systems, long-termism.
In other words, even if the world changes quickly, as long as there is the blessing of systematic and probabilistic thinking, we can work harder in the right direction of a high probability.
And probabilistic thinking is not difficult, as long as you find the right book to read.
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Part of the source network, intrusion and deletion.
I am @ Chu Xisi reading and painting, thanks for reading and looking forward to attention.