>>11707305Identity of the first orb affects the final result regardless of what the second is
If you got G first then you still can either have GS or GG after the second pick
If you got S first then you still can either have GS or SS after the second pick
It means that you can get GS from two different points, either from picking G after S or picking S after G, while both GG and SS has exactly one way - if you pick both G or both S
It means that probability of GS is twise as big as GG or SS, so system of equasiosn is like this GS+GG+SS = 1; GG=SS; GS = 2GG
Solving it will give you GG = SS = 1/4 and GS = 1/2
Other way to think about it is to realise that GS and SG are ALWAYS different states which exist under the surface regardless of what we think, and thus we can only think of them as the same by purposefully merging them into one, which means merging(summing) their probabilities too, thus we get SG1/4(true state) + GS1/4(true state) = GS1/2(merged state we pretend to be true)
And with those probabilities when you remove SS you will have a total of 3/4 instead of 1 and thus GG being 1/4 its 1/4 out of 3/4 which is 1/3
