If I have a domain of 0 to 1000000 (but I doubt the domain matters, just that the ranges can overlap). I then chose 1% ranges uniformly, allowing for ranges to overlap completely or partially.

How do I find the expected percent of the domain that will be covered after K selections?

This seems like a simple selection with replacement but since the ranges can overlap I'm not sure how to find it. Is it as simple as repeatedly adding the useful part of the next selection? The first selection covers 1% if the domain. The second selection also covers 1% of the domain but since only 99% is uncovered, the expected coverage of the second selection is 0.99%, thus after 2 selections it is 1.99%...and so on with decreasing returns on each selection?