Title pretty much says it all. Everything I read about WWI armies makes enlistment sound like a one way trip. It seems as though you had to fight until the war was over or you were physically incapable of fighting anymore (as opposed to modern armies, where you fight for a period of time and then go home). Is this accurate? Would someone fighting in the Battle of the Frontiers still have been fighting by the Somme, if they were still alive? If so, how many of those first soldiers made it to the end?
I don't have a history degree but I work for YouTube channel exclusively focused on World War I, so I hope I can still write an answer acceptable to the mods. We're getting this question once a week at least and I find it interesting because for me, whoever works with sources from the war, I can't remember any author ever thinking of doing this kind of math. The reason for that is twofold:
A: In case of the German Army (to various degrees in all the other WW1 armies too) we don't have the exact numbers. For example, an allied bomb hit the military archive in Potsdam during World War 2 and destroyed vast amounts of files, including personal records. But more importantly, we don't even know the exact numbers of casualties (or even enlisted men).
World War I has a high number of "Missing in Action" casualties due to various factors like artillery usage, weather or the lack of agencies like the War Graves Comissision at the outbreak of the war. The German Volksbund Deutsche Kriegsgräberfürsorge only has estimates about how many German soldiers are still missing along the Western Front. And that is just one front. Germany fought: on the Western Front, Eastern Front, Romanian Front, Macedonian Front, Italian Front, Palestine, German East Africa, German Southwest-Africa, Togoland, Kamerun, Tsingtao, the Bismarck Archipelago, German New Guinea, German Samoa (and that's just the land based theaters since you only asked about infantry).
Just to give you an idea what it was like to work as a soldier tasked with even finding soldiers to bury:
"Often I have picked up the remains of a fine brave man on a shovel. Just a little heap of bones and maggots to be carried to the common burial place. Numerous bodies... seemed quite whole, but which became like huge masses of white slimy chalk when we handled them. I shuddered as my hands, covered in soft flesh and slime, moved about in search of the (identity) disc, and I have had to pull bodies to pieces in order that they should not be buried unknown. It was very painful to have to bury the unknown."
On top of that "seriously injured" is a relative term. I assume you include Shellshock ("Kriegszittern")? But do you also include things like malnutrition for German soldiers in 1918? And do you stop counting after the armistice in November 1918 or after signing the Treaty of Versailles?
So just from thinking about what numbers you want to use for calculating the chance, you run into a lot of problems that historians run into every day when working with primary sources and archives.
B Forgive me for asking so bluntly (I am German), but why is the mathematical chance important for your understanding of World War I? It surely is a tough subject to wrap one's head around. But if I would say that 7% (made up number) of German infantry soldiers got through World War I unharmed. How would this change your perspective vs. 25%(made up number)? Is 25% a "better" experience for the soldiers involved?
Numbers surely are important to understanding history but they can only do so much. I personally like historians like Peter Hart who emphasize personal stories and primary sources from "smaller people" within these big historic events which make it easier to understand.
A well sourced article examining the myriad of problems concerning identification, exhuming, burial of dead soldiers: http://www.vlib.us/wwi/resources/clearingthedead.html