How to break into a math book

100% of the 10 challengers have been infected with the M virus since they entered the hospital.From the appearance point of view, there is no difference between infected people and healthy people, and the only way to distinguish them is through a doctor's diagnosis.

But the doctor's diagnosis is not completely accurate, and there will be a 10% misdiagnosis rate in the diagnosis process.In the end, according to the judgment of doctors, 18 infected people were selected.

Of course, not all of these 18 people carry the M virus, and some were misdiagnosed by doctors.Similarly, the 18 healthy people opposed to the 82 people are not necessarily completely healthy. For healthy people, doctors may still have the possibility of misdiagnosing them.He may misjudge a healthy person as an infected person, and he may misjudge an infected person as a healthy person.

That's why Tu Hua said that "healthy people are not necessarily healthy".

The tall boy in the opposite camp of healthy people finally understood after hearing what Tu Hua said: "Are you saying that among those of us who have been diagnosed as healthy, there may be misdiagnosed infected people?"

Tu Hua nodded: "So no camp is safe."

The boy thought for a while and said: "If the misdiagnosis rate is 10%, rounding off the 18 people diagnosed as infected by the doctor, 2 people are healthy, and among the people diagnosed as healthy, about 8 people are infected by the doctor. infected?"

The girl standing next to him wondered: "But according to your calculation, there are 18-28=24 people who are actually infected, which does not meet the figure of 10% infection rate at all."

涂化回过头，对那个18个疑似被感染者道：“虽然说医生的误诊率是10%,但却不代表你们每个人的被误诊率为10%。你们18个人里面，只有9个人是真正感染了M病毒的,也就是说虽然被医生诊断为感染者,但你们真正被感染的概率只有50%。”

The crying girl among the infected people quickly raised her head: "Ten out of 100 people are real infected people, and we have 10 people here, does it mean that there is still one person in the team of healthy people?"

The healthy camp on the opposite side immediately became restless. The tall boy seemed a little dissatisfied and looked at Tu Hua provocatively: "Why do we have to believe what you say?"

This probability question is actually not difficult, but the infection rate and misdiagnosis rate are both 10%, which can easily lead to misunderstandings.

Tu Hua explained: "In fact, these two 10% probabilities seem to be related, but in fact they are independent of each other. The 10% infection rate and the 10% misdiagnosis rate do not affect each other, that is to say, even if the doctor does not Misdiagnosis will not affect the 10% infection rate of M virus."

"It's easy to think about it. Out of 100 people, under the influence of a 10% infection rate, 10 people are really infected and 90 people are healthy people. This number is something that doctors can't change. "Tu Hua casually took a pen from the doctor's check-in column in the corridor, and marked his thoughts on the white wall, "Now that 10 infected people have been confirmed, let's analyze the doctor's misdiagnosis rate .”

"The misdiagnosis rate is 10%. That is to say, for these 10 infected people, in the doctor's judgment, he will judge that 9 people are infected and 1 person is healthy. , right in your team." Tu Hua pointed to the camp of the healthy people opposite, and continued to explain, "For the 1 healthy people who are really healthy, the doctor's misdiagnosis rate is still 90%, which means that there are 10 apparently healthy people were misdiagnosed as infected by him, and only 9 truly healthy people were diagnosed correctly."

“这样计算下来，被医生诊断为感染者的18人就包括健康者中被误诊的9位和感染者中被确诊的9位；而被医生判定为健康者的82人中，包括确实健康的81位和明明携带病毒，却被误诊的1位。”

Tu Hua's explanation was indeed very reasonable, and the people who were clamoring just now were immediately speechless.But soon they discovered the paradox in this probability game: "Only getting such a probability does not seem to allow us to find the real infected person."

连那个“宁可错杀一千”的高个子男生都纠结起来：“如果说18个人里有9个感染者，我们还能直接把这18个人交出去，可要在剩下的82人里找出唯一的那1个被感染者，总不能把82个人都处决了吧？”

This is the unsolvable paradox created by virus programs.In fact, the normal level should be over after Tu Hua makes a correct analysis, but now it has become that they are asked to select infected persons who have no characteristics at all based on probability, which is impossible at all.

Tu Hua was also caught in a tangle.After a while, the doctor wandered out of the office again, looking at everyone with malicious intent: "Have you not found the infected person yet? An hour is almost up, the virus will continue to infect..."

Everyone became uneasy, only Su Gechi calmly stroked his chin in thought.Tu Hua approached him and asked, "What did you think of?"

Su Gechi frowned and said, "I'm thinking about how the virus programmed the challenger who entered the hospital to be infected."

Tu Hua didn't quite understand, so Su Gechi explained to him: "If the system asks you to find the infected person, it means that the moment you enter the game, the system has selected 10 people and written the infection program for them. .So that the doctor NPC can pick out 10 infected people based on a 18% misdiagnosis rate."

"So there is actually a difference between the infected and the healthy?" Tu Hua was astonished.

Su Gechi nodded, and called up the system program screen to try to crack it: "But I don't have permission to enter the challenger's program now, so I have no way of judging how the infected program behaves."

Tu Hua glanced at the NPC doctor who was chattering: "Does he know?"

Su Gechi smiled, he knew that Tu Hua looked serious, but in fact he would always come up with some wretched and rogue ideas: "You can try it."

He had just been promoted to fight, and the violent factor in Tu Hua's body had already started to cause trouble. The doctor's cheap look really deserved a beating. It's time for him to hone his hands and feet.

Tu Hua stared at him, crossed his arms and walked over.Perhaps it was because Tu Hua's expression was too penetrating, a trace of fear flashed across the NPC doctor's face: "You...what are you doing?"

Tu Hua looked at him with a smile, and rushed out with a punch, directly embedding him in the opposite wall.

The other challengers were stunned, looking at him with fear in their eyes.A girl whispered to the person next to her: "In this game... can I still beat NPCs?"

The person next to her gasped: "Then you have to have such fighting power."

Tu Hua didn't hear what they said, he pulled out the blood-stained doctor embedded in the wall: "Now you know what I'm going to do?"

The doctor's nose was bruised and his face was swollen, and his eyelids were drooping pitifully: "You, you, you, you, you will never pass the level if you kill me!"

Tu Hua smiled: "We can't pass the level without killing you. Since we can't pass the level no matter what, it's better to kill you."

The doctor wants to cry but has no tears. Are these challengers also infected with the virus?Why are they all more violent than NPCs!He looked at Tu Hua aggrievedly: "Then what are you going to do?!"

Tu Hua casually threw him on the ground with a calm expression: "Tell me the difference between an infected person and a healthy person."

This cunning doctor NPC quickly crawled back, eyes dodging: "I... I don't know!"

Tu Hua raised his fist again.

The doctor immediately ran away with his head in his arms, and looked at Tu Hua with tears in his eyes: "Don't hit me—I said!"

He wiped the blood off his face aggrievedly: "On the right hand of the infected person... there is a red mole."

As soon as he said this, everyone raised their right hands to look.Most of the people were overjoyed. Among the 18 infected people, 9 people were safe. They excitedly raised their right hands and ran towards the healthy people.

Some of the remaining 9 people were desperate, while others were relieved, quietly waiting for the system's trial.

The tall boy was also safe. He looked at everyone excitedly: "Is there another one? Who is the infected person mixed with the healthy people?"

Tu Hua slowly stretched out his right hand, and saw a red mole the size of a mung bean at the junction of his wrist and palm, emitting a lustrous light.He looked up at Su Gechi, his face pale: "I... I was also infected."

The camp was instantly clear, and 90 healthy challengers were sent out of the checkpoint, only Tu Hua and the other 9 challengers remained in the hospital.The nine challengers got together, their bodies were slowly pixelated, and they were about to disappear.

They didn't know what they were about to face, and thought they could return to real life after being eliminated. The girl who was still crying just now showed a relieved smile, saying that she had had enough of this perverted game, and would rather make more books Five-year college entrance examination and three-year simulation.

Tu Hua and Su Gechi stood together, not wanting to reveal the cruel truth to them.He is not afraid of being eliminated, nor is he afraid of floating in the abyss, he just feels a little guilty.

The opportunity he had finally won, he had agreed to keep walking and rescued all the challengers, but he fell on the first stone steps.

Tu Hua looked at Su Gechi apologetically, and whispered, "I'm sorry..."

Who knew that Su Gechi suddenly pinched his wrist, rubbing his fingers at the red dot: "Who said you would be eliminated?"

Tu Hua who was just immersed in grief:? ? ?

Su Gechi touched the red mole on his wrist, then brought up the system panel, and modified the code cracklingly: "I said that you were pulled out of the abyss by me, so the programs on your body were all written by me later." Written. A small infection program... easy to clean up."

As soon as he finished speaking, the red dot on Tuhua's wrist faded, but within two to three seconds, the red mole completely disappeared.Tu Hua looked at Su Gechi in shock, and stammered, "This...is this okay?"

Su Gechi put away the system panel and glanced at him: "There is nothing wrong."

So the two of them easily left the level called [Virus and Infected].Tu Hua opened his own system interface, and the number on the customs clearance probability has indeed changed:

[Current Level: Probability Level]

[Main task: unknown]

[Clear rate: 1/52]

52 in 2?It's strange that the clearance rate this time is not expressed in percentages, but in fractions.Although Tu Hua had passed the level, he did not expect the system to still generously give him a clearance rate of nearly [-]%, which made him very satisfied.

After coming out of the [Virus and Infected] level, Tu Hua fully realized what he was going to face next.If the previous levels were all based on brains and wisdom, the next level may be dominated by luck.After all, the purpose of that virus program is to destroy the original rules of the game, and it will try its best to prevent the challenger from clearing the level.

Tu Hua glanced at Su Gechi beside him, thinking that luckily there was a cheater with him.In the past, he looked down on people who bought cheats in the game, but now he felt that it was really important to have a high-level cheat in the face of such a perverted and irregular virus program.

While he was feeling emotional, Su Gechi suddenly pointed to the classroom in front of him: "I suggest you go to this level."

There was a line of words [Three Doors of Probability] floating at the door of the classroom. It couldn't be seen from the words. Tu Hua asked strangely: "Why did you go to this place?"

Su Gechi raised his lips: "Because I have a role in this level."

This classroom is at the corner of the first floor, and no one seems to have visited it.Just as Tu Hua pushed open the door, he felt a strong light flash in front of his eyes, which made him unable to open his eyes.

He raised his hand to cover his eyes, and subconsciously turned back to look for Su Gechi, only to find that the person who had been following him had disappeared.

There was a vast expanse of whiteness in front of him, Tu Hua hurriedly called out Su Gechi's name, squinted his eyes, and ran around looking for it.But the only thing that responded to him was a steady stream of echoes, as if he had been thrown into a deserted valley and lost Su Gechi.

Is it because Su Gechi is the NPC of this level, so after entering the level, he completes his task?

I don't know if it's because the eyes have adapted to the light, or if the surrounding light has faded, Tu Hua slowly sees the surrounding scene clearly.This is not a valley, nor is it empty as imagined.

This is the mirror world.

There are mirrors of different sizes all around Tu Hua. He stands alone in the center, but casts countless shadows in the mirrors.He raised his hand, and thousands of people in the mirror also raised their hands. He called out Su Gechi's name loudly, and the other people in the mirror also opened their mouths, and their voices echoed in their ears one after another.

Not only will countless painted figures be projected, but his voice can also be copied.

【Ding--】

[Submission: The Three Doors of Probability]

[Mission rules: Find Mr. X hiding behind the door.There are three doors in total. The challenger chooses a door at will, and Mr. X stands behind one of the doors. If he chooses the right one, he will pass the level, and if he chooses the wrong one, he will be eliminated. 】

In the next moment, all the paint in the mirror disappeared, and three ancient doors appeared in front of him.

Tu Hua tried to touch it. Although he disappeared in the mirror, the three doors were still in the mirror world.That is to say, although he can see it, he cannot touch it.

Just when he was thinking about how to open the three doors, a man in a clown suit suddenly appeared in the mirror world.He has a red nose, white paint on his face, and a strange laugh: "Welcome, welcome, welcome! You look delicious boy, which door do you want to choose?"

Tu Hua didn't answer his words, but looked at him coldly: "Where's Mr. X?"

The clown grinned: "Mr. X is behind one of the doors! You choose quickly, and I can eat you after you choose... Oh no, no, you can see Mr. X after you choose!"

The clown looked crazy, probably also affected by the virus.But now Su Gechi is indeed not by his side, and he also said before entering the level that he has a role in this level.

So the scene he was talking about was hiding behind the door and waiting for the challenger to be rescued?

Tu Hua didn't know what tricks the virus-infected system would play, but at present, he did have to follow the rules.There are three doors here, and Su Gechi is locked behind one of them. Since the clown and the door are both behind the mirror, Tu Hua cannot touch or approach it, so it is impossible to identify which door Su Gechi is behind through the details.

So his only way to tell is to guess the probability.

There are three doors, and the probability of Su Gechi appearing behind each door is one-third.There are no prompts, conditions, or restrictions, so the probability of Sugechi appearing behind each door is equal.

In this way, the coating cannot guarantee the accuracy at all.

So he's still gambling with his luck.Fortunately, Tu Hua had thought of this a long time ago. He didn't have too much expectation for the virus-infected system. With the idea that there must be a way for the car to reach the mountain, Tu Hua chose a door at random.

He pointed to the door on the far right and said, "I choose this."

The clown didn't expect him to make a decision so quickly, he jumped to the door on the right and knocked: "Are you sure you choose this one?"

Tu Hua nodded: "OK."

The clown rolled his eyes and looked very regretful: "You child is really unlucky! Why don't you let me help you with a method of elimination!"

He jumped to the door in the middle again, and shook his hand exaggeratedly: "I can help you eliminate this door, there is no Mr. X behind it! Do you want to change the answer now?"

Tu Hua frowned: "Are you sure what you said is right?"

The clown raised three fingers and swore: "Of course! I am a professional NPC!"

Tu Hua did hesitate.

Although it seems that the probability of Mr. X appearing behind each door is one-third, but if the clown helps him do the elimination method, the probability will change.

In the door selected by Tu Hua, the probability of Mr. X appearing is one-third, which means that the sum of the probability of Mr. X appearing after the other two doors is two-thirds.At this time, the clown ruled out a wrong answer for him, so the leftmost door, that is, the door that the clown didn't rule out and Tuhua didn't choose, has already occupied two-thirds of the probability.

Many people think that if one door is excluded, there are only two doors left, and the probability of Mr. X appearing after each door becomes [-]/[-], and some people think that the probability of each door is still [-]/[-].

But when the right door is chosen for the first time, the probabilities appear randomly.After the clown excludes a wrong answer, the probability that the subject has been artificially intervened, the right door is randomly selected, and the left door is left after the human intervention, so the probability of the left door and the right door is naturally different.

The clown's intervention is to change the probability distribution.

So calculated in this way, the probability of Mr. X appearing in the door on the left is two-thirds, and the probability of the door on the right is one-third. From the perspective of probability alone, Tu Hua must change the answer.

However, there is a great deal of uncertainty in this question.

Tu Hua hesitated for a while, then asked the clown, "Do you know which door Mr. X is behind?"

The clown smiled and opened his big mouth, showing his ferocious teeth: "Of course, otherwise, how can I help you eliminate it?"

If the clown knows and there is no malice, Tu Hua's choice to change the answer at this time is correct.But he wasn't sure if the clown would intentionally frame him. Knowing that Mr. X was behind the right door that Tu Hua had chosen at the beginning, he deliberately misled Tu Hua and tempted him to change his answer.

But if he insists on choosing the door on the right, he may fall into the trick of the clown's double inducement.The clown probably expected Tu Hua's mentality and knew that Tu Hua would not believe him, so he made a special appearance to rule out the second door.In this way, even though Tu Hua thinks that the door on the left has a high probability, he is afraid that the clown will deliberately deceive him, and insists on choosing the door on the right without Mr. X.

He didn't know what the clown was thinking, so it was still an unsolvable problem.

Tu Hua struggled for a long time, and finally decided to follow the mathematical theory and choose the door with a two-thirds probability.So he changed his answer and chose the left door.

The clown seemed very happy after hearing his answer, and hurriedly jumped over and pushed open the door on the left, and there was nothing behind the door.

"You guessed wrong..." The clown showed a ferocious expression, and walked forward step by step, as if he wanted to go through the mirror and come to Tu Hua, "You guessed wrong, so I want to eat you..."

Did he guess wrong?

But the clown's behavior couldn't help but make him suspicious.The Joker seemed to be anxiously awaiting his choice, as if no matter what he chose, the door would be empty.

Tu Hua felt a little weird, took a step back, and said to the clown, "Open the other two doors and show me."

The clown's expression was a little unnatural: "You have lost, why should I satisfy your request?"

really!

The clown resisted so much, it must be because the other two doors are also empty!So where the hell is Suge Chi?Didn't he say that this level is his level? Why did it disappear from the beginning, and didn't even appear at the last moment?

Could it be... What did the virus program do to him?

Tu Hua was so anxious, his anger made him unable to think rationally, he clenched his fists and shouted at the clown: "Mr. X, where is he?!"

The clown looked at him with a grin, and bared his teeth: "Hehehe...Actually, I have already eaten him!"

Tu Hua's brain went blank, all the despair and anger in his heart gathered on his fist, he glared at the clown angrily, smashed the mirror in front of him with his fist, and shouted with red eyes: "Give me back my Mr. X!" I--"