Using your theory:
You assume that the one without lumps doesn't have a cancer since there's no presence of lumps.
I assume he may have a cancer since there's no evidence that he's healthy.
I can provide a real example of how scientists think:
It's been confirmed that there was water on Mars, therefore scientists assume organics are still there (yet they haven't found anything).
No.
First and foremost, you are missing the rather important distinction between
evidence and
proof.I am not assuming one without lumps has no cancer. The person without lumps is simply
less likely to have cancer than one with lumps. Hence: it is evidence. I don't know how often cancer manifests itself in lumps compared to not, thus I don't know the precise amount by which to adjust the probability downward, but downward it goes.
Suppose you have ten thousand possible worlds. One person, again, has lumps. The other does not. The amount of worlds in which the former has cancer is considerably greater than the amount of worlds where the latter has cancer. Thus: if there is no outward evidence of cancer, it is evidence that the person does not have cancer. That doesn't mean they shouldn't visit a doctor to make sure. It's
evidence, not
proof.