If amateur fiction is not your thing skip to the bottom.
As IP (Implausible Physics) expert for DREAM, the Department for Reckless Engineering and Advanced Megalomania you have been tasked by sheikh Shanzaar himself with ascertaining the safety of a new system of bridges joining for the first time Ping and Pong, the two main land masses of the glorious seafaring nation of Ha'Lful. The bridges span an archipelago of 12 artificial islands representing the twelve tribes of Ha'Lful.
Ping
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Pong
A top two finisher of the In-God-We-Trust school of cost conscious design you are burdened with preserving your nations proud tradition of putting safety first and never ever countenancing anything less than 50% reliability. Inspecting the individual bridges you are filled with joy and gratitude in finding that every one them has precisely a fifty percent chance to stand tall for decades and a fifty percent chance to collapse within the first two weeks.
Leave it to Nos'Y'Meddlar to ruin the moment. "Safety is all nice and well." he says with the infuriating faux modesty that has been his since he narrowly outscored you in the In-God-We-Trust school's final exams. "But I'm worried for the ordinary men and women who are asked to foot the bill. What will they get out of this?" lilts the descendant of the mighty Y'Meddlar dynasty and heir of half the country's arable land. "Ha!" you say raising your voice a little more and drawing a bit more attention than would be wise. "You claim to care for our brave citizens. And yet you forget how much easier their lives will be once they can freely cross between Ping and Pong." "But that is exactly my concern." he says unable to hide a swell of triumphalism while gradually turning away from you and towards the growing audience your little exchange has drawn "With only half the bridges available to them will they actually be able to cross from Ping to Pong?"
A few hours and quite a few drinks later the pang of public humiliation stubbornly refusing to ebb away you find little comfort in having worked out exactly what you should have replied.
Question: In the picture after randomly removing bridges each with 50 percent probability what are the odds of there still being a path from Ping to Pong?
Source: A former colleague of mine who has moved on. I do, however, half suspect that this (minus my embarrassing stab at making a back story) is kind of a classic, so maybe one of the regulars on this site happens to know a reference (hopefully not a duplicate)?
