Doctors flunk quiz on screening-test math (2014)

I find the article's use of percentages frustrating. We know people find it hard to understand percentages, so this article should give the question twice - the first using percentages and the second using natural frequencies.

"A machine has been invented to scan a population for a disease. The machine is good but not perfect. If you have the disease there is a 90% chance it will return positive. If you do not have the disease there is a 1% chance it will return positive. About 1% of the population have the disease. Mr Smith is tested, and the test comes back positive. What's the chance Mr Smith actually has the disease?"

(This is from "Reckoning with Risk" by Gerd Gigerenzer).

Most people cannot get the right answer from this question.

If you reword the question they can.

"Think of a group of 100 people. 1 of them has a disease. The entire group is screened. The one person who has the disease tests positive. Of the 99 people who don't have the disease one person will also test positive. How many people of those who test positive have the disease?"