Random Magic Paths - is it truly random?

[alexti]

Saber Cherry said:
Furthermore, unless I'm just up too late and should really go to bed now (probably true), it seems that the chances of 20 random picks missing a least one path (in other words, getting 20 consecutive sages and still not having 8 paths between them) is 43.6%, which is relatively high. Math:

1-((1-.0692)^8), where the .0692 is derived from the same calculation as above.

0.0692 is probability of not getting particular path. Then 1-0.0692 is probability of getting that particular path. Then you consider that events of getting/not getting some path are independent from each other. But those events are not independent. Consider, that your first event (getting blood path has happened on your serie, but that serie happened to have astral too). This makes the probability of your second event (getting astral) = 1, not 1-0.0692.

Code:

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p(missing at least one of the paths) =

= p(missing path A) + p(missing path B) - p(missing path A and path B) + p (missing path C)+ ... = 

= sum[i=1..8]((-1)^(i+1)*C(i,8)*p(i)), where p(i)= ((8-i)/8)^20.

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This comes to around 46.94%, which is even "relatively higher"

[bone_daddy]

So has anybody here managed to create an infinite improbability drive yet?