In fact bald people have the same number of hairs as anyone else -- they are just very short and fine hairs, more like those on "naked" parts of the body. I believe humans actually have more hairs than the other more obviously hairy apes.
Each hair, on whatever part of the body, grows from one of a group of half a dozen follicles. It starts as a very fine hair, gets thicker, grows for a bit, then stops. It stays like that for some time, then falls out and the follicle rests for a while. Each follicle in the group takes turns, so there are usually one or two fully developed hairs, one beginning to grow, and a couple of resting, empty follicles.
The differences between the hairs on different parts of the body is all to do with how thick they grow, and how long they grow for before stopping -- some grow for years, others just for weeks.
As baldness develops, the thickness and length of the hairs decrease, but the total number remains the same. In the normal "male pattern" baldness it happens because the man has follicles which are more sensitive to testosterone -- this is why bald men tend to be more hairy elsewhere.