How many units do you use to attack a dead zone in Axis and Allies?
If I'm attacking a dead zone I won't use tanks. So I determine the attacking force structure by determining the number of aircraft available for the attack and then adding infantry until my gut (or a battle calculator) tells me I'll have enough to occupy the territory. 

Often, I'll find that absent these dead zone attacks my planes wouldn't have anything else to do anyway, so more often than you might expect dead zone attacks utilize overwhelming airpower.

Against 1 infantry with 2 fighters: I'd probably send two infantry because this almost guarantees I can capture the territory (with one fighter I'd still only send 2 inf--stranding 3 inf in a dead zone is too many and the odds of winning are still decent). If I'm stretched thin I might only send one, but I'd prefer occupying the territory with two infantry than not taking it at all. If you take it you get 3 IPCs that turn and you make the other side answer the more difficult question of how many inf they send to re-take the territory. 

Against 2 infantry: the problem is more difficult. Typically in this scenario I'm almost resigned to not capturing it with high probability and only want to make sure I take enough infantry that there's no chance of taking fighter damage. So if I can afford it I'll attack with 3 inf, knowing that I'm going to retreat before any combat round when I don't have at least as many infantry has he does.

As for specific probabilities I target in my attack structure, that's all game dependent and balanced against the opportunity cost of those units elsewhere on the board. My key metric in planning dead zone attacks is minimizing downside (i.e. the risk of losing fighters and/or stranding more than 2 inf in the dead zone).