There is still a big difference between high school knowledge and university, especially mathematics, and if you change to other college students or teachers, you may not be able to make up for high school students. Pen ~ fun ~ pavilion www.biquge.info

But Li Mingxuan is different, because of his cultivation since childhood, his memory is very rebellious, almost to the realm of unforgettable, the books he has read, he can remember them once, and it is even more impossible to forget what he has learned.

Sister-in-law Wu asked Li Mingxuan to tutor her daughter in mathematics, so Li Mingxuan subconsciously thought that Chen Jiayao's mathematics was not good, but when he finished reading Chen Jiayao's mathematics test paper, he found that this was not the case.

High school mathematics contains a lot of knowledge, such as sets and functions, trigonometric functions, inequalities, solid geometry, plane analytic geometry, permutations and combinations, and so on.

The exam paper in his hand was obviously a comprehensive paper, containing all the parts of knowledge, similar to the type of high school examination paper.

What makes Li Mingxuan strange is that Chen Jiayao's other parts of the questions are very good, and the error rate is very low, only the permutation and combination part, but almost none of them are correct, and even the simplest questions are wrong.

"Did you not learn this part well?" After reading the test paper, Li Mingxuan asked with some doubts.

Seeing that Li Mingxuan didn't start to calculate, but just found his own problem after reading it once, Chen Jiayao nodded in surprise, thinking that Teacher Li was really powerful.

Speaking of permutations and combinations, Chen Jiayao's mood was a little depressed.

From the first semester of high school to the first semester of her sophomore year, her math scores were among the best in her class. But just last semester, the original math teacher in their class was transferred, and the school transferred a new math teacher to them.

Chen Jiayao swore that if she knew that the male teacher was a small-bellied and narrow-minded person, she would not point out the mistake of his lecture in class.

In short, since then, the male teacher who thinks that Chen Jiayao has embarrassed herself in front of her classmates will ask her to answer some very difficult questions in class, and if she can't answer it, she will be criticized as an example of not listening well in class......

This directly led to Chen Jiayao's complete loss of interest in math class, and it just so happened that the male teacher taught permutations and combinations last semester......

"Actually, it's not difficult to permutate and combine, such as this question." Li Mingxuan pointed to a question on the test paper and said.

Chen Jiayao looked down at the question Li Mingxuan was pointing to.

"There are 100 balls in the bag, 40 white balls, 60 black balls, and if you don't put back and take 20 balls, the probability of getting the white ball for the twentieth time is __."

This is the last question of the fill-in-the-blank question, and it is also recognized by the students in the class as the most difficult one in this test paper, and Chen Jiayao remembers that the best students in the class did not do it at that time.

"What do you think is the probability of getting a white ball for the first time?" Li Mingxuan looked at her and asked.

"It's 40/100, of course." Chen Jiayao answered without thinking about it.

This question is so simple that even someone who has not studied math can answer it.

If it weren't for Li Mingxuan's serious face, Chen Jiayao would have wondered if he was going to humiliate himself.

"And what about the second time?" Li Mingxuan continued to ask.

"The second time?"

This question is not difficult, Chen Jiayao picked up the pen and calculated on the scratch paper.

“40／100。” The first time the white ball was taken and the first time the black ball was taken, and two minutes later, Chen Jiayao calculated the answer.

"How can it be the same as the first answer!" There was something strange about her.

"And guess what the probability of getting the white ball for the twentieth time is?" Li Mingxuan said with a smile.

"Guess?" Chen Jiayao's eyes widened. "Can you guess that?"

??

If this question can be "guessed" correctly, none of the top math students in their class will be able to do it!

For the first time, Chen Jiayao began to doubt Li Mingxuan's teaching level.

However, looking at him with a serious face, not like a joke, Chen Jiayao thought for a while and said, "It won't be 40/100, right?" ”

This time, she was just talking nonsense, and in her opinion, the calculation steps of this problem must be particularly complicated, and the answer will not be as simple as she had calculated before.

Li Mingxuan didn't answer Chen Jiayao's question directly, smiled, looked at her and said: "Let's change the question - if there are a hundred red envelopes in a box, but 60 red envelopes are empty, and all the students in your class draw out a red envelope in turn, what is the probability that you will get the real red envelope?" ”

“40／100。” Chen Jiayao said the answer in one mouth, and asked with some doubts: "This has nothing to do with the number of people, right?" The probability should be the same for everyone. ”

This is the problem of drawing lots in real life, you don't have to think about it at all, according to common sense, you also know that the probability of everyone getting a red envelope is the same.

Faintly, Chen Jiayao felt as if there was a bright light in her mind, but she couldn't catch it.

Li Mingxuan smiled and said, "What if you are the twentieth person?" ”

What if I'm the twentieth person?

As soon as Li Mingxuan's words fell, a lightning bolt immediately crossed Chen Jiayao's mind, and the thoughts that were still a little vague just now instantly became clear.

That's right, if you replace the red envelope with the ball of the question just now, aren't the two questions the same?

Therefore, whether it is the first, second or twentieth time, the probability of getting the white ball is the same as the probability of drawing the red envelope every time, which is 40/100!

Chen Jiayao is not stupid, on the contrary, she is very smart and understands everything, Li Mingxuan just gave an example, and she immediately understood his intentions.

"Alright, let's move on to the next question." Seeing that Chen Jiayao had already understood, Li Mingxuan nodded and smiled, and directly pointed to the next question.

……

……

"Okay, I've pointed out all the wrong questions on this test paper, and if you digest it after you go down, there should be no problem." After finishing the last question, Li Mingxuan stood up and stretched his body and said.

"Huh? That's it? Chen Jiayao woke up like a dream, looked down at the electronic watch on her wrist, and found that an hour had passed.

At this time, she was surprised to find that she had just been completely immersed in Li Mingxuan's explanation, and the permutations and combinations and probability problems that she hated the most had become so vivid and interesting when she came out of Li Mingxuan's mouth!

He often just gives a few simple examples in life, and he can connect the topic with the knowledge points in the textbook, and through his in-depth explanation, the obscure questions become simple and easy to understand - Chen Jiayao never knew that the original lecture could still be like this?

The permutations and combinations that she had always found incomprehensible were so simple!

silently compared Li Mingxuan with their small-bellied math teacher, Chen Jiayao immediately said sorry to Li Mingxuan in her heart.

How can you compare that guy to Teacher Li!

After Li Mingxuan left Chen Jiayao's room, she immediately picked up a pen and paper from the table and began to seriously recalculate the mistakes that Li Mingxuan had just talked about.

Outside the door, the landlord's sister-in-law gently closed the door for her daughter with a smile on her face.

At this time, Li Mingxuan, who had finished washing, was already sitting cross-legged on the bed, guiding the true qi in his body to circulate along the meridians.