If you were a healthy American male of age serving in a branch of the military from 42 to 45, what are the chances you were never shot at?
I don't have a number for you, but I can say that there were many jobs to be done in the military that didn't involve combat.
In the Canadian Army of the Second World War, it reached a point where it took 7 support personnel (ie. Service Corps, administration) to support one infantryman (Source: Burns, Manpower in the Canadian Army 1939-1945). Some criticized this large "tail" vs. "teeth" ratio as an overly bureaucratic waste, but I imagine it was much the same in the American Army. Combat roles were becoming more technical, and fitness and training more important, so, there had to be a large support base, and thus, many veterans who were in roles where they never faced combat.
I tried to find specific numbers of military personnel that saw combat but couldn't find anything of that nature.
However, the full numbers should give you a rough idea:
So a total of 962,403 (5.9%) of the service personnel were casualties. That's neither here/there but it does help to paint the picture.
[This source gives total US Army Ground Forces numbers in comparison to the total US Army personnel].(http://www.historyshots.com/usarmy/backstory.cfm) This maintains that the US Army fielded a 35% ratio of infantry/combat element to support personnel. If you were drafted and went into the Army, there is a good chance you wouldn't even end up in a Ground Forces unit. If you were a healthy young male (teens/20s) you'd be more likely to end up in infantry.
An overwhelming number of USAAF personnel were support on bases so that serves to skew any figures. These were mechanics, armorers, etc. However, the personnel that did go up and fight had egregious casualty rates.
USN was a crap-shoot. There were a lot of hazardous jobs but in the timeframe you're giving ('42-45) a bulk is out of the way and you're likely to serve in '43-45 on an active ship. It's still hazardous but in terms of "being shot at" it's relatively low. Kamikazes were the major threat and predominately towards screening ships/carriers.
USMC is probably your worst bet. The Marines had a far higher ratio of Ground Combat forces compared as the USMC (still does) rely on the USN for a lot of logistical support that allows them to maintain a higher number of combat-capable troops.
I'd say that if you were a healthy male given a dice roll to determine service branch and job duty you'd have 60-70% chance of not getting fired at? I haven't found any other scholarly source to specifically tackle this subject.