Reshaping life starting from the Junior Class of HKUST

Chapter 56 Math Problems for Lottery Tickets

Wu Zhe and his brothers greeted each other, picked up their computer, and left gracefully.Finally, I can go back to my dormitory.

Temporary accommodation is okay, but it is not as comfortable as your own dormitory.

It was not until midnight on the third day that the three of them returned to the dormitory.Wang Chao and Wu Zhe woke up as soon as they entered the dormitory.

Sitting up from the bed, he asked, "I'm back! How do you feel!"

"My body has been hollowed out! My feet are soft." This is Huang Minghai's reply.Wu Zhe was amused when he heard the "puchi", if he hadn't known Huang Minghai's character, he would have thought he was driving.

"Azhe, what are you laughing at? Anyway, I won't participate in the next fight. I'm still young, and I can't grow taller if I stay up late." Wang Chao muttered.

"Tired!" Shen Zhiwen also spoke.

After the three of them finished talking, they touched their own beds.

"I said brothers, you sleep without washing!" Wu Zhe finished asking.None of the three returned him.After a while, the three people's voices rose up one after another.

When the three of them woke up, it was already afternoon.

The arrangement of the Higher Education Society Cup Mathematical Simulation Competition is very humane.The game time is Thursday, Friday, Saturday and three days.Sunday is just right for you to rest.

Wu Zhe was reading in the dormitory when he saw them awake.Putting down the book in his hand, he said: "There is bread on the table. I don't know when you woke up. I didn't bring you any food. I guess you will be hungry when you wake up. I bought some bread from the supermarket."

A few people came out of the wash, took a few bites of bread and went down.Finally fully recovered.

Wu Zhe saw Wang Chao taking a piece of paper to write and draw, and it turned out to be a mathematical formula.Smiling to Wang Chao: "Why, I still want to do the question!"

Wang Chaotou didn't raise his head and said, "Didn't I choose the lottery question? I'm more interested in it than the lighting question. This is not empty, let's do the math. Let's buy a lottery ticket later."

Hearing what Wang Chao said, Huang Minghai and Shen Zhiwen also became interested.Young people are quite curious about winning the lottery.

Besides, there is no need for the two of them to do digital and analog calculations. Isn't there Wang Chao?Wang Chao can't do it, and there is another great god Wu Zhe here?So watching the excitement is not a big deal.

"Calculate it carefully. If it works, I'll give you ten yuan. It's up to you to win the lottery!" Huang Minghai said with a smile.

"Twenty." Shen Zhiwen also said aloud.

"Hehe, I can't figure this out for a few hours. By the time Wang Chao does his calculations, the lottery shops have already closed." Wu Zhe was clearly dampening everyone's enthusiasm.

When Wu Zhe finished speaking, the three pairs of eyes looked at Wu Zhe pitifully.

Being stared at by the three of them, Wu Zhe could only raise his hands.Then he grabbed the pen and paper on the table.

"I'm scared, you guys can do it! Don't look at me like that again! You just finished the competition, and you still want to do the questions. When Wang Chao came back last night, you said that you would kill him and not participate in the future? You are good, and you will do it as soon as you recover today." Question." Wu Zhe kept counting his hands while talking.

"By the way, what lottery do you use as the standard?" Wu Zhe looked up at Wang Chao.

"Traditional lottery and lottery. This model will come out, and other lotteries will be similar." Wang Chao replied.

Wu Zhe nodded and stopped talking.

The few people didn't speak any more, Wang Chao didn't count, and leaned back in his chair.This is ready to lie down, just watch Wu Zhe's performance.

After about half an hour, Wu Zhe threw away the pen, pushed a stack of draft paper in front of the three of them, and said, "Okay, let's have a look!"

This speed scared the three of them a little.

Wang Chao snatched it up and said, "It's so fast, are you sure it's done?"

Wu Zhe didn't speak, but pouted towards the draft paper.

The three of them glanced roughly, and Huang Minghai said, "Ah Zhe, you better explain it! It's too sloppy."

Wu Zhe thought about how he wrote simply and sloppily in pursuit of speed, and said, "Okay! Let me explain to you."

“传统型彩票我们经过计算很容易得到一等奖到六等奖的获奖概率。解题公式我纸上有，说下结果。一等奖的概率是2*10的负7次方；二等奖是8*10的负7次方………六等奖3.42*10的负3次方。概率多低不用我多说了吧！”

"Okay, let's look at the lotto type again. The probability calculation of the lotto type is also very interesting, especially the special numbers in it, such as the first "33 to choose 7" (m to choose n) plan, the second prize is It is guaranteed that there are 6 identical basic numbers and the same special numbers, then the probability is the number of possible cases that meet the requirements of the second prize divided by the total number of cases. The total number of cases is fixed, which is the case of C mn C*m^nC.

满足二等奖要求的可能的情况数是从中奖号码的7个基本号中任选6个的情况数目，特别号要一样那就只有一种情况，表述成从1-26中除实际特别号码以外的25个数里抽了0个，所以满足二等奖要求的可能的情况数就是C n n 1 C m n 1 0 C_n^{n-1}*C_{m-n-1}^0C——
From this, it can be concluded that there are 29 alternatives.Therefore, before buying a lottery ticket, it is necessary to judge whether the awards and bonus amounts are reasonable.A reasonable plan must satisfy: the single bet of the high prize is higher than that of the low prize, the bonus difference must be within a reasonable range, and the single bet of the first prize must be between 60 and 500 million.

Then with this constraint, we will make a preliminary selection of 29 schemes.Well, I drew a sketch of the diagram, yes, that's the one. "

After the three of Wang Chao looked at it and nodded, Wu Zhe continued to explain:

“用上面的约束条件筛选后，可以得到1、6、23、24、25、27这几种方案是不合理的。”

"Then take out some reasonable ones, and we can use the linear evaluation model to draw conclusions.

Total Expected Payoff for Low Term Prize:
E j low=∑ i = 4 7 qijpij E^{low}_j=\sum_{i=4}^7q_{ij}p_{ij}
Expected payoff for a lottery ticket:

E j = E j high + E j low = 1 E_j=E^{high}_j+E^{low}_j=1
So the expected loss per lottery bet is

E loss =( E j 2 ) RMB = 1 RMB E_{loss}=(E_j-2)RMB=-1 RM
2)RMB=1RMB
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Wu Zhe glanced at a few people, saw them nodding, and said with a smile:
"Two yuan a bet, the worst is not winning the prize, the net loss is 2 yuan, the best is winning the first prize and no one will share the first prize, and the highest prize is capped at 500 million, so the range of income It is 2 → 500 million-2o500 million 2→500 million. But the distribution of income is extremely uneven, and the probability is almost all in the interval of 2 → 0 -2o02→0. So the value is a negative number.

Now I say brother three, do you still want to buy lottery tickets?In fact, I don't object to contributing to national welfare! "

Wang Chao asked Huang Minghai and Shen Zhiwen, "Do you want to buy it or not? Even if it is calculated like this, isn't there still a probability? This model is a large number analysis, and small probability problems are still possible. Maybe I am God's own son?"

Huang Minghai and Shen Zhiwen looked at Wang Chao with the eyes of a foolish son.This is so clear, still buy?

"You don't have to be God's own son, you just need to be your father's own son. Your family's money is not much more than winning the lottery!" Wu Zhe joked about Wang Chao.

"Hey, is this a question of money or not? This is a question of right or wrong." Wang Chao shouted.

　I'm going crazy, this document can't type equations, and mathematical formulas, and I insist on explaining mathematical problems in Chinese.I originally wanted to solve the lottery problem for everyone, but it didn't look like it.Do not spray professionally.I did my best.Don't know what to do next time you write a math problem?Finally, I advise everyone to play less lottery.

　　
　
(End of this chapter)