1. Start with possible values (imprecise)
The value probabilities of the three scatterers are 3, 4, 5, 6, ..., 18, respectively, of which 3 ~ 10 * * 8,1~18 * * 8 each account for exactly half.
2. Start with the average (imprecise)
The average number of points obtained by one particle is (1+6)/2 = 3.5, so the average number of points obtained by three particles is 3 x 3.5 = 10.5, which is just the middle value between 10 and 1 1.
Step 3 refute
Assuming that the two probabilities are different, we assume that the probability of 3~ 10 is relatively small. Today, there is a naughty child. The points on the three scatterers change from 1, 2, 3, 4, 5, 6 to 6, 5, 4, 3, 2, 1. In other words, the original scatterers all changed from X point to 7-x point.
Then the original three scatterers add up to 3x, which becomes 2 1-3x.
In the past, the probability of 3~ 10 was relatively small, but now the probability of (21-10) ~ (21-3) is small, that is,1~18.
But if you think about it carefully, the original experimental method of sowing seeds is the same as the current experimental method, which is made of three grains with a score of 1~6, but the probability of 3~ 10 is relatively small, and now it is118 after being corrected by naughty children, which is a small contradiction!
So only two probabilities are equal.
4. Violence Law
Lists all additions from 3 to 10.
3 = 1+ 1+ 1
4 = 2+ 1+ 1
4 = 1+2+ 1
4 = 1+ 1+2
5 = 1+ 1+3 (3 species)
5 = 1+2+2 (3 kinds)
6 = 1+ 1+4 (3 kinds)
6 = 1+2+3 (6 species)
6 = 2+2+2
7 = 1+ 1+5 (3 species)
7 = 1+2+4 (6 species)
7 = 1+3+3 (3 kinds)
7 = 2+2+3 (3 kinds)
8 = 1+ 1+6 (3 species)
8 = 1+2+5 (6 species)
8 = 1+3+4 (6 species)
8 = 2+2+4 (3 kinds)
8 = 2+3+3 (3 kinds)
9 = 1+2+6 (6 species)
9 = 1+3+5 (6 species)
9 = 1+4+4 (3 species)
9 = 2+2+5 (3 kinds)
9 = 2+3+4 (6 kinds)
9 = 3+3+3
10 = 1+3+6 (6 species)
10 = 1+4+5 (6 species)
10 = 2+2+6 (3 kinds)
10 = 2+3+5 (6 species)
10 = 2+4+4 (3 kinds)
10 = 3+3+4 (3 kinds)
Add up to *** 108 species.
And all the possibilities ***6x6x6 = 2 16.
The conclusion is that 3~ 10 accounts for half, and 1 1~ 18 naturally accounts for the other half.