I think I would welcome any number of false positives, so long as they were presented with appropriate statistics. For example, if the system told me I had a 1

I think I would welcome any number of false positives, so long as they were presented with appropriate statistics. For example, if the system told me I had a 1% chance of having a cancer somewhere, due to a small lump, I could decide if it's worth pursuing. On the other hand, if it told me I had a 99.99% chance of having a rapidly growing cancer somewhere, I'd go to the doctor. The big things would be caught early. The little things -- they could be tracked. If I have a pinhead-sized growth, and it's staying fixed, it's probably okay. If it's doubling every day, I might want to get it checked out.