Still quoting Niederman & Boyum:

The most common answer was 95 percent. The correct answer is 2 percent, and it was given by only 18 percent of the alleged medical experts.

I think I understand the reasoning here, which I'll state in what I have just learned is a frequentist mode.

out of 1000 people:
1 person will have the disease (.1 percent)
50 will test positive, but will not have the disease (5% false positive rate

OK, here's my question:

What are we comparing when we come up with an answer of 2%? (And is 'comparing' the right word here?)

1/50
or
1/51

Both ratios give you a probability of 2%, obviously, but I want to know which ratio is correct. (And is it a ratio?! I'm finally beginning to read on Hung Hsi Wu, and I gather he says that ratios aren't fractions.)

Frankly, I have no idea what the precise relationship among 'percents,' 'rates,' and 'ratios' is.

Both Ed and I feel that we ought to divide 1 by 51 in order to get the 'probability' that a person with a positive test has the disease--but are we confusing 'probability' with 'percent'?

I realize I don't know what the definition of probability is, apart from the standard 'probability that the outcome is not due to chance' definition I learned in psych courses in college.