The mathematical problem in lottery is mainly the probability of winning.
Combination games such as welfare lottery have special combination formulas to calculate, and only the probability of sports lottery is discussed here.
(1) First of all, the probability of the grand prize is easy to calculate. There are seven numbers from 0000000 to 9999999 * * 107, and there is only one grand prize number, so the winning probability of the grand prize is 10-7.
(2) Now discuss the winning probability of the first to fifth prizes. For the convenience of description, the following provisions are made:
The number of a certain number is the same as the winning number, which is represented by "0"; If they are different, they are represented by "X", and both numbers can be represented by ".".
1. The first prize has two forms:10.
A. There are only 9 cases.
Therefore, there are nine first prize numbers, in the form of "XX XX XX XX XX XX First Prize Number".
B In the same way, there are nine first prize numbers, in the form of ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
So * * * has 18 first prize numbers. So the winning probability of the first prize is18×10-7 =1.8×10-6.
2. There are three forms of second prize:
A.for??，
∵× has 9 seeds and 10 seeds.
∴ * * There are 9× 10 = 90 situations, that is, * * has 90 second prize numbers in the form of ∴∴∴∴∴.
B. For XXX,
∵ Each× has 9 seeds.
∴ * * There are 9× 9 = 8 1 cases, that is, * * has 8 1 second prize number in the form of ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
C. For {\ \ lang1033,} ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
There are 90+8 1+90 = 26 1 second prize numbers * *.
The winning probability of the second prize is 26/kloc-0 /×10-7 = 2.6/kloc-0 /×10-5.
3. There are four forms of the third prize:1
Similar to the reasoning of 1 2, it can be concluded that there are 900 ××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××
The third prize number * * * is 900+810+810+900 = 3420.
The probability of winning the third prize is 3420×10-7 = 3.42×10-4.
There are five forms of the fourth prize:1
There are 9000 ×××, 8 100××××, 8 100××××, 8100, 8100.
However, ∫ single note number can only win the biggest prize in one note, and× is calculated twice in the above algorithm.
∴ The total number of the fourth prize is 9000× 2+8100× 3-9 = 42291.
The probability of the fourth prize is 4229/kloc-0 /×10-7 = 4.2295438+0×10-3.
There are six forms of the fifth prize: 16.
In the same way, we know that there are 90,000 81000×××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××× However, these numbers include шт and 81уууууууууууууууууу.
The winning number of the fifth prize is 90000× 2+81000× 3-90× 2-81× 4-810× 2-729 = 420147.
The winning probability of the fifth prize is 420147×10-7 = 0.045438+047.