There are 20 garments on a clothes line each
garment supported by two pegs.
The pegs were randomly picked out of a set of 20 green and 20
red pegs.
What is the probability that n garments are supported by two pegs of the same colour?
Provide a list for 21 possible values of n.
Source: Australian Joe Kupka
(In reply to
computer assisted solution by Charlie)
This is the probability matrix for each step from 1 to 20 of choosing pins for each garment. The probabilities initailly diffuse from the certainty of no pairs of either color before pegging begins, and then coalesces on the main diagonal at the end of 20 choices for 20 garments:
green pairs
red
pairs 0 1 2 3 4 5 6 7 8 9 10
0 0.5128205 0.2435897 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.2435897 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.2633403 0.2494802 0.0530146 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.2494802 0.1316701 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0530146 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.1354321 0.1918622 0.0807841 0.0100980 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.1918622 0.2031482 0.0479655 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0807841 0.0479655 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0100980 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0697681 0.1313281 0.0820801 0.0201600 0.0016380 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.1313281 0.2093042 0.0984961 0.0136800 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0820801 0.0984961 0.0261630 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0201600 0.0136800 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0016380 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0360093 0.0843969 0.0695033 0.0250984 0.0039629 0.0002180 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0843969 0.1800466 0.1265953 0.0347516 0.0031373 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0695033 0.1265953 0.0675175 0.0105496 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0250984 0.0347516 0.0105496 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0039629 0.0031373 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0002180 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0186255 0.0521514 0.0529663 0.0249253 0.0057121 0.0006013 0.0000225 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0521514 0.1396914 0.1303786 0.0529663 0.0093470 0.0005712 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0529663 0.1303786 0.1047685 0.0325946 0.0033104 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0249253 0.0529663 0.0325946 0.0058205 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0057121 0.0093470 0.0033104 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0006013 0.0005712 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000225 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0096577 0.0313874 0.0376649 0.0215789 0.0063467 0.0009520 0.0000668 0.0000017 0.0000000 0.0000000 0.0000000
1 0.0313874 0.1014056 0.1177029 0.0627749 0.0161841 0.0019040 0.0000793 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0376649 0.1177029 0.1267570 0.0588514 0.0117703 0.0008092 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0215789 0.0627749 0.0588514 0.0211262 0.0024521 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0063467 0.0161841 0.0117703 0.0024521 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0009520 0.0019040 0.0008092 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000668 0.0000793 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000017 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0050220 0.0185427 0.0254963 0.0169975 0.0059757 0.0011248 0.0001094 0.0000049 0.0000001 0.0000000 0.0000000
1 0.0185427 0.0703079 0.0973494 0.0637406 0.0212469 0.0035854 0.0002812 0.0000078 0.0000000 0.0000000 0.0000000
2 0.0254963 0.0973494 0.1318272 0.0811245 0.0239027 0.0031870 0.0001494 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0169975 0.0637406 0.0811245 0.0439424 0.0101406 0.0007968 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0059757 0.0212469 0.0239027 0.0101406 0.0013732 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0011248 0.0035854 0.0031870 0.0007968 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0001094 0.0002812 0.0001494 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000049 0.0000078 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000001 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0026202 0.0108082 0.0166280 0.0124710 0.0049884 0.0010912 0.0001284 0.0000076 0.0000002 0.0000000 0.0000000
1 0.0108082 0.0471630 0.0756574 0.0581980 0.0233831 0.0049884 0.0005456 0.0000275 0.0000005 0.0000000 0.0000000
2 0.0166280 0.0756574 0.1238030 0.0945717 0.0363737 0.0070149 0.0006235 0.0000195 0.0000000 0.0000000 0.0000000
3 0.0124710 0.0581980 0.0945717 0.0687794 0.0236429 0.0036374 0.0001949 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0049884 0.0233831 0.0363737 0.0236429 0.0064481 0.0005911 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0010912 0.0049884 0.0070149 0.0036374 0.0005911 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0001284 0.0005456 0.0006235 0.0001949 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000076 0.0000275 0.0000195 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000002 0.0000005 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0013725 0.0062385 0.0105275 0.0086379 0.0037791 0.0009070 0.0001181 0.0000079 0.0000002 0.0000000 0.0000000
1 0.0062385 0.0308806 0.0561465 0.0491282 0.0226745 0.0056686 0.0007558 0.0000506 0.0000015 0.0000000 0.0000000
2 0.0105275 0.0561465 0.1080820 0.0982563 0.0460577 0.0113373 0.0014172 0.0000810 0.0000016 0.0000000 0.0000000
3 0.0086379 0.0491282 0.0982563 0.0900683 0.0409401 0.0092115 0.0009448 0.0000337 0.0000000 0.0000000 0.0000000
4 0.0037791 0.0226745 0.0460577 0.0409401 0.0168878 0.0030705 0.0001919 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0009070 0.0056686 0.0113373 0.0092115 0.0030705 0.0003378 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0001181 0.0007558 0.0014172 0.0009448 0.0001919 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000079 0.0000506 0.0000810 0.0000337 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000002 0.0000015 0.0000016 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0007224 0.0035756 0.0065012 0.0056885 0.0026255 0.0006564 0.0000875 0.0000059 0.0000002 0.0000000 0.0000000
1 0.0035756 0.0198647 0.0402260 0.0390070 0.0199098 0.0055135 0.0008205 0.0000625 0.0000022 0.0000000 0.0000000
2 0.0065012 0.0402260 0.0893911 0.0938607 0.0511967 0.0149324 0.0022973 0.0001758 0.0000059 0.0000001 0.0000000
3 0.0056885 0.0390070 0.0938607 0.1042896 0.0586629 0.0170656 0.0024887 0.0001641 0.0000037 0.0000000 0.0000000
4 0.0026255 0.0199098 0.0511967 0.0586629 0.0325905 0.0087994 0.0010666 0.0000444 0.0000000 0.0000000 0.0000000
5 0.0006564 0.0055135 0.0149324 0.0170656 0.0087994 0.0019554 0.0001467 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000875 0.0008205 0.0022973 0.0024887 0.0010666 0.0001467 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000059 0.0000625 0.0001758 0.0001641 0.0000444 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000002 0.0000022 0.0000059 0.0000037 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000001 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0003824 0.0020396 0.0039262 0.0035693 0.0016731 0.0004118 0.0000515 0.0000029 0.0000001 0.0000000 0.0000000
1 0.0020396 0.0126199 0.0280443 0.0294465 0.0160617 0.0046847 0.0007207 0.0000552 0.0000018 0.0000000 0.0000000
2 0.0039262 0.0280443 0.0709870 0.0841328 0.0515313 0.0168648 0.0029279 0.0002574 0.0000103 0.0000002 0.0000000
3 0.0035693 0.0294465 0.0841328 0.1104243 0.0736162 0.0257657 0.0046847 0.0004183 0.0000161 0.0000002 0.0000000
4 0.0016731 0.0160617 0.0515313 0.0736162 0.0517614 0.0184040 0.0032207 0.0002510 0.0000065 0.0000000 0.0000000
5 0.0004118 0.0046847 0.0168648 0.0257657 0.0184040 0.0062114 0.0009202 0.0000460 0.0000000 0.0000000 0.0000000
6 0.0000515 0.0007207 0.0029279 0.0046847 0.0032207 0.0009202 0.0000863 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000029 0.0000552 0.0002574 0.0004183 0.0002510 0.0000460 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000001 0.0000018 0.0000103 0.0000161 0.0000065 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000002 0.0000002 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0002040 0.0011600 0.0023200 0.0021267 0.0009667 0.0002175 0.0000223 0.0000008 0.0000000 0.0000000 0.0000000
1 0.0011600 0.0079544 0.0191402 0.0212669 0.0119626 0.0034800 0.0005075 0.0000335 0.0000007 0.0000000 0.0000000
2 0.0023200 0.0191402 0.0546863 0.0717758 0.0478505 0.0167477 0.0030450 0.0002719 0.0000105 0.0000001 0.0000000
3 0.0021267 0.0212669 0.0717758 0.1093726 0.0837384 0.0334954 0.0069782 0.0007250 0.0000340 0.0000006 0.0000000
4 0.0009667 0.0119626 0.0478505 0.0837384 0.0717758 0.0314019 0.0069782 0.0007477 0.0000340 0.0000005 0.0000000
5 0.0002175 0.0034800 0.0167477 0.0334954 0.0314019 0.0143552 0.0031402 0.0002991 0.0000093 0.0000000 0.0000000
6 0.0000223 0.0005075 0.0030450 0.0069782 0.0069782 0.0031402 0.0005981 0.0000374 0.0000000 0.0000000 0.0000000
7 0.0000008 0.0000335 0.0002719 0.0007250 0.0007477 0.0002991 0.0000374 0.0000000 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000007 0.0000105 0.0000340 0.0000340 0.0000093 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000001 0.0000006 0.0000005 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0001098 0.0006589 0.0013385 0.0011898 0.0004908 0.0000892 0.0000056 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0006589 0.0049970 0.0128494 0.0147232 0.0081796 0.0022085 0.0002677 0.0000112 0.0000000 0.0000000 0.0000000
2 0.0013385 0.0128494 0.0412251 0.0588930 0.0414091 0.0147232 0.0025766 0.0002008 0.0000052 0.0000000 0.0000000
3 0.0011898 0.0147232 0.0588930 0.1030627 0.0883394 0.0386485 0.0085886 0.0009202 0.0000418 0.0000006 0.0000000
4 0.0004908 0.0081796 0.0414091 0.0883394 0.0901798 0.0463782 0.0120777 0.0015337 0.0000863 0.0000017 0.0000000
5 0.0000892 0.0022085 0.0147232 0.0386485 0.0463782 0.0270540 0.0077297 0.0010352 0.0000575 0.0000010 0.0000000
6 0.0000056 0.0002677 0.0025766 0.0085886 0.0120777 0.0077297 0.0022545 0.0002761 0.0000108 0.0000000 0.0000000
7 0.0000000 0.0000112 0.0002008 0.0009202 0.0015337 0.0010352 0.0002761 0.0000230 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000052 0.0000418 0.0000863 0.0000575 0.0000108 0.0000000 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000006 0.0000017 0.0000010 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0000599 0.0003744 0.0007488 0.0006084 0.0002028 0.0000223 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0003744 0.0031450 0.0085176 0.0097344 0.0050193 0.0011154 0.0000837 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0007488 0.0085176 0.0306633 0.0468467 0.0334619 0.0112934 0.0016731 0.0000837 0.0000000 0.0000000 0.0000000
3 0.0006084 0.0097344 0.0468467 0.0936933 0.0878375 0.0401543 0.0087838 0.0008365 0.0000261 0.0000000 0.0000000
4 0.0002028 0.0050193 0.0334619 0.0878375 0.1054050 0.0614863 0.0175675 0.0023528 0.0001307 0.0000022 0.0000000
5 0.0000223 0.0011154 0.0112934 0.0401543 0.0614863 0.0442701 0.0153716 0.0025096 0.0001765 0.0000044 0.0000000
6 0.0000000 0.0000837 0.0016731 0.0087838 0.0175675 0.0153716 0.0061486 0.0010980 0.0000784 0.0000016 0.0000000
7 0.0000000 0.0000000 0.0000837 0.0008365 0.0023528 0.0025096 0.0010980 0.0001882 0.0000098 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000261 0.0001307 0.0001765 0.0000784 0.0000098 0.0000000 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000022 0.0000044 0.0000016 0.0000000 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0000333 0.0002130 0.0003994 0.0002662 0.0000541 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0002130 0.0019968 0.0055910 0.0060569 0.0025958 0.0003569 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0003994 0.0055910 0.0227135 0.0363417 0.0249849 0.0071385 0.0006692 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0002662 0.0060569 0.0363417 0.0832830 0.0832830 0.0374773 0.0071385 0.0004462 0.0000000 0.0000000 0.0000000
4 0.0000541 0.0025958 0.0249849 0.0832830 0.1171167 0.0749547 0.0218618 0.0026770 0.0001046 0.0000000 0.0000000
5 0.0000000 0.0003569 0.0071385 0.0374773 0.0749547 0.0655853 0.0262341 0.0046847 0.0003346 0.0000070 0.0000000
6 0.0000000 0.0000000 0.0006692 0.0071385 0.0218618 0.0262341 0.0136636 0.0031231 0.0002928 0.0000093 0.0000001
7 0.0000000 0.0000000 0.0000000 0.0004462 0.0026770 0.0046847 0.0031231 0.0008365 0.0000837 0.0000023 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0001046 0.0003346 0.0002928 0.0000837 0.0000065 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000070 0.0000093 0.0000023 0.0000000 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000001 0.0000000 0.0000000 0.0000000 0.0000000
1
0 0.0000190 0.0001212 0.0001940 0.0000808 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0001212 0.0012932 0.0036370 0.0033946 0.0009194 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0001940 0.0036370 0.0169728 0.0275807 0.0165484 0.0030339 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000808 0.0033946 0.0275807 0.0735486 0.0758470 0.0303388 0.0037923 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0009194 0.0165484 0.0758470 0.1264117 0.0853279 0.0227541 0.0018962 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0030339 0.0303388 0.0853279 0.0910164 0.0398197 0.0068262 0.0003555 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0037923 0.0227541 0.0398197 0.0265464 0.0071107 0.0007111 0.0000198 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0018962 0.0068262 0.0071107 0.0027088 0.0003809 0.0000169 0.0000001
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0003555 0.0007111 0.0003809 0.0000635 0.0000026 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000198 0.0000169 0.0000026 0.0000000 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000001 0.0000000 0.0000000 0.0000000
1
0 0.0000114 0.0000685 0.0000727 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0000685 0.0008729 0.0023277 0.0014548 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0000727 0.0023277 0.0130933 0.0203673 0.0082742 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000000 0.0014548 0.0203673 0.0661937 0.0661937 0.0182033 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0082742 0.0661937 0.1365246 0.0910164 0.0170656 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0182033 0.0910164 0.1228721 0.0546098 0.0068262 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0170656 0.0546098 0.0477836 0.0136525 0.0010666 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0068262 0.0136525 0.0073138 0.0012190 0.0000508 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0010666 0.0012190 0.0003428 0.0000254 0.0000003
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000508 0.0000254 0.0000021 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000003 0.0000000 0.0000000
1
0 0.0000076 0.0000361 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0000361 0.0006504 0.0013821 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0000000 0.0013821 0.0110565 0.0138207 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000000 0.0000000 0.0138207 0.0644965 0.0524034 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0000000 0.0524034 0.1572101 0.0864656 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0864656 0.1729311 0.0648492 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0648492 0.0864656 0.0216164 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0216164 0.0185283 0.0028951 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0028951 0.0014475 0.0001206 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0001206 0.0000268 0.0000007
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000007 0.0000000
1
0 0.0000076 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
1 0.0000000 0.0007226 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
2 0.0000000 0.0000000 0.0138207 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
3 0.0000000 0.0000000 0.0000000 0.0921378 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
4 0.0000000 0.0000000 0.0000000 0.0000000 0.2620169 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
5 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.3458623 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
6 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.2161639 0.0000000 0.0000000 0.0000000 0.0000000
7 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0617611 0.0000000 0.0000000 0.0000000
8 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0072376 0.0000000 0.0000000
9 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0002681 0.0000000
10 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000013
1
Obtained by moving the reportage within the For...Next loop.
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Posted by Charlie
on 2016-06-08 13:27:03 |
step-by-step diffusion and coalescence of the probabilities
