Wu Zhe said hello to his brothers, put on his computer, and left in style. I can finally go back to my dorm.

Temporary accommodation is ok, but it's not as comfortable as your own dormitory.

It wasn't until the middle of the night on the third day that the three returned to their dormitories. As soon as Wang Chao and the three of them entered the dormitory, Wu Zhe woke up.

He sat up from the bed and asked, "You're back!" How does it feel! ”

"The body is hollowed out! My feet are all soft. This is Huang Minghai's reply. Wu Zhe listened to the "poof" and was happy, if he didn't know Huang Minghai's character, he would think that he was driving.

"Ah Zhe, what are you laughing at? Anyway, I won't participate in the next killing. I'm still young, and I can't stay up late. Wang Chao muttered.

"Tired!" Shen Zhiwen also spoke.

After the three of them finished speaking, they went to their bed.

"I said brothers, you can sleep without washing!" Wu Zhe asked. None of the three replied to him. After a while, the voices of the three of them rose one after another.

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

The arrangement of the Higher Education Society Cup Digital Simulation Competition is still very humane. The competition is held on Thursday, Friday and Saturday. Sunday is just the right time to rest.

Wu Zhe was reading a book in the dormitory when he saw them wake up. Put down the book in his hand and said: "There is bread on the table, I don't know when you will wake up, I didn't bring you food." I suppose you're going to get hungry and buy some bread from the supermarket. ”

A few people washed up and took a few bites of bread. It's finally fully recovered.

Wu Zhe saw Wang Chao taking a piece of paper and writing and drawing, and at first glance, it was a mathematical formula. smiled at Wang Chao: "What, I still want to do the question!" ”

Wang Chao didn't raise his head and said: "Didn't you choose that lottery question, I'm much more interested in it than the lighting problem." It's not empty, do the math. We'll buy lottery tickets later. ”

Hearing Wang Chao say this, Huang Minghai and Shen Zhiwen were also interested. Young people are still quite curious about winning the lottery.

Besides, they don't need to do digital and analog calculations, isn't there a Wang Chao? Wang Chao can't do it, there is still a great god Wu Zhe? So it's not a big deal to watch the excitement.

"Do the math, if it's okay, I'll give you ten dollars. It's up to you to win! Huang Minghai said with a smile.

"Twenty." Shen Zhiwen also said out loud.

"Hehe, I can't figure it out in a few hours. By the time Wang Chao is settled, the lottery shops have closed. "Wu Zhe, this is obviously discouraged from 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 like this, Wu Zhe could only raise his hands. Then he grabbed the pen and paper on the table.

"I'm scared, you can do it! Don't look at me like that again! You've just finished the contest and you're still thinking about it. Wang Chao came back last night, and you still said that you won't participate in the future? You're good to do the questions as soon as you recover today. Wu Zhe said, his hand did not stop.

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

"Traditional lottery and lotto type, this model is going to come out, and other lotteries are similar." Wang Chao replied.

Wu Zhe nodded and stopped talking.

A few people didn't speak again, and Wang Chao didn't count anymore, and leaned back in the chair. This is ready to lie flat, just watch Wu Zhe perform.

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

This speed scared the three of them a little.

Wang Chao snatched it and said, "So fast, are you sure you're done?" ”

Wu Zhe didn't speak, and pouted at the scratch paper.

The three of them swept it roughly, and it was still Huang Minghai who said: "Ah Zhe, you should talk about it!" It's too scribbled. ”

Wu Zhe thought that he had written simply and scribbled in order to pursue speed, so he said, "Okay! I'll tell you about it. ”

"In the traditional lottery, we can easily get the probability of winning the first prize to the sixth prize after calculation. I have the formula for solving the problem on paper, let's talk about the result. The probability of the first prize is 2*10 to the minus 7th power; The second prize is 8*10 to the minus 7 power......... The sixth prize is 3.42*10 to the minus 3 power. I don't need to say more about how low the probability is! ”

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

The number of possible cases that meet the requirements of the second prize is the number of cases where 6 of the 7 basic numbers of the winning number are selected, and the special number is the same, then there is only one case, which is expressed as 0 from the 25 numbers in 1-26 in addition to the actual special number, so the number of possible cases that meet the requirements of the second prize is C n n − 1 ∗ C m − n − 1 0 C_n^{n-1}*C_{m-n-1}^0C

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From this, it can be concluded that there will be 29 options. Therefore, before buying lottery tickets, you must first judge whether the prize and prize amount are reasonable. A reasonable scheme must be satisfied: the single bet of the high prize is higher than that of the lower prize, the difference in prize money must be within a reasonable range, and the single bet of the first prize must be between 600,000 and 5 million.

So with this constraint in mind, let's make a primary selection of 29 options. Well, I drew a simple diagram, yes, that's it. ”

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

"After filtering with the above constraints, it is unreasonable to get 1, 6, 23, 24, 25, and 27."

"Then take out the reasonable ones, and we can draw conclusions using a linear evaluation model.

Total expected return of the Junior Prize:

E j Low=∑ i = 4 7 q i j p i j E^{Low}_j=\sum_{i=4}^7q_{ij}p_{ij}

Expected payout of a ticket:

E j = E j high + E j low = 1 E_j = E^{high}_j + E^{low}_j=1

So the expected loss per ticket is:

E l o s s =( E j − 2 ) R M B =− 1 R M B E_{loss}=(E_j-2)RMB=-1 RM

−2)RMB=−1RMB

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Wu Zhe glanced at a few people, and when he saw them nodding, he smiled and said:

"Two dollars a bet, the worst is not to win, the net loss of 2 yuan, the best is to win the jackpot and the first prize is only one of their own no one to share, take the highest prize capped at 5 million, so the range of income is − 2 → 5 million - 2o 5 million - 2→5 million. However, the distribution of returns is extremely uneven, and the probabilities almost all fall in the range of − 2 → 0 -2o0−2→0. So the value is negative.

Now I said, brother, do you still want to buy lottery tickets? In fact, I have no objection to contributing to the welfare of the country! ”

Wang Chao said to Huang Minghai and Shen Zhiwen, "Do you want to buy it?" Even if this is calculated, isn't there still a probability? This kind of model is a large number analysis, and the problem of small probability is still possible. Maybe I'm God's own son? ”

Huang Minghai and Shen Zhiwen looked at Wang Chao with the eyes of their stupid son. It's so clear, still buy?

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

"Hey, is it a matter of money or not? It's a question of whether it's a hit or a hit. Wang Chao shouted.