What are the odds of a chick dying in the first year? How in the world do you answer that? What are the odds of you having a fender bender the next time you drive to the store? That depends on how you drive and some just plain luck. If you deal with living animals at some point you will deal with dead animals. That’s just nature.
I generally hatch my own instead of buying them. Of the ones I’ve received through the mail I’ve only lost one, a 12 week old Speckled Sussex cockerel that ate like he was a meatie. I’m sure he ate himself to death. If you are only getting four, you probably won’t be getting them through the mail though but are more likely to get them at a feed store or someplace local. Very few places ship that few chicks through the mail. That means they should be in pretty good health to start with. Of the ones I hatch, most make it. If I lose any it is usually during the first two weeks. Some are just not meant to make it no matter what you do. I don’t expect to lose any, whether I get them in the mail or hatch them myself, but sometimes stuff happens.
You don’t have a lot of control over what happens before you get the chicks so you can’t be sure what shape they are in when you get them. There is some luck involved with that. But if you start with healthy chicks and provide food, water, protection from the environment, protection from predators, and appropriate heat they normally do really well. Keeping the brooder dry really helps too.
In your circumstances and with your restrictions I’d start with three and expect all three to make it. But if one doesn’t, and that is a possibility, you still have two so they can keep each other company. And you have room to bring in two more whenever you want to.
But you don’t necessarily have to kill a hen when she no longer lays as well as you want. If you feel you can, run an ad on Craigslist and give them away. Someone will take them. The odds are a spent hen will be eaten but you lose control when you no longer have possession. That way you don’t have to kill then yourself. If you think you can do this, I’d start with four or five and thin as needed in the future.