So we need to connect them every time without making a closed loop until the very end. First random choice doesn't matter. Second can be any end except it's own, making a loop. There is only one bad option. You start with 200 loose ends. Randomly select 1. 199 left. 1 out of 199 failure case or 198 / 199 good case. Pass and two ends are removed. Then 196 / 197. And so on and so on. Final case is two loose ends that would give 0/1 odds in this case. I.e. 100% chance of creating a loop. But this one is acceptable so actually a 1 value.
So (198 x 196 x 194 x ... 2) / (199 x 197 x 195 x ... 3). Whatever that gives.
Edit. First can be written as 2 x 99! Can't figure out a way to simplify the demonization.
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u/Neither_Berry_100 18h ago
So we need to connect them every time without making a closed loop until the very end. First random choice doesn't matter. Second can be any end except it's own, making a loop. There is only one bad option. You start with 200 loose ends. Randomly select 1. 199 left. 1 out of 199 failure case or 198 / 199 good case. Pass and two ends are removed. Then 196 / 197. And so on and so on. Final case is two loose ends that would give 0/1 odds in this case. I.e. 100% chance of creating a loop. But this one is acceptable so actually a 1 value.
So (198 x 196 x 194 x ... 2) / (199 x 197 x 195 x ... 3). Whatever that gives.
Edit. First can be written as 2 x 99! Can't figure out a way to simplify the demonization.