Probability table with n=5 attempts, starting with g green and b=15 total balls
(rows sum to 1)

        s (number of successes)
        0           1           2           3           4           5           6
g start
0       1           0           0           0           0           0           0
1       0.708246    0.291754    0           0           0           0           0
2       0.488946    0.438600    0.072454    0           0           0           0
3       0.327680    0.483797    0.174104    0.014420    0           0           0
4       0.212084    0.462386    0.274015    0.049462    0.002054    0           0
5       0.131687    0.401982    0.352000    0.104691    0.009481    0.000158    0
6       0.077760    0.323563    0.397037    0.174617    0.026074    0.000948    0
7       0.043151    0.242261    0.405689    0.250272    0.055309    0.003319    0
8       0.022133    0.168149    0.380523    0.320790    0.099556    0.008849    0
9       0.010240    0.107034    0.328533    0.374993    0.159289    0.019911    0
10      0.004115    0.061248    0.259556    0.402963    0.232296    0.039822    0
11      0.001348    0.030434    0.184691    0.397630    0.312889    0.073007    0
12      0.000320    0.012342    0.114726    0.356346    0.391111    0.125156    0
13      0.000042    0.003612    0.058548    0.282469    0.451951    0.203378    0
14      0.000001    0.000572    0.021570    0.186943    0.474548    0.316365    0
15      0           0.000020    0.004148    0.089877    0.431407    0.474548    0