[SlowToady]

and they have their passports and things all ready, when all of a sudden, they are kidnapped by Evil Trolls. The Gnomes are (conveniently) named 1 through 100. Now, the Evil Trolls take the passports of the Gnomes, and put them into a cave. The Evil Trolls then explain the rules to the following game they are going to play with the Gnomes. Each Gnomes passport is put into a separate box, labeled 1 through 100. The Gnomes are brought in to the cave containing the boxes one at a time and allowed to open at most 50 boxes. If the Gnome sees his passport, this is good. If not, then the Evil Trolls will eat the Gnomes for dinner. If only 1 Gnome doesn't find his passport, all of them are eaten for dinner. The passports are all put back, and all the boxes closed prior to each Gnome entering. The Gnomes are not allowed to communicate in any way once the first Gnome has entered the cave.

What is the probability that the Gnomes are eaten for dinner?