*Jacked from researchers at the Univ. of Toronto …*

“Although intelligence as measured by IQ tests is important, so is the ability to think rationally about problems.

The surprise is that less intelligent people usually perform just as well as highly intelligent people on problems that test rationality.”

Below is a question to test if you’re a rational (i.e. logical) thinker … or just smart

Question

The XYZ virus causes a disease in one in every 1,000 people.

A test always correctly indicates if a person is infected.

The test has a false-positive rate of five per cent.

In other words, the test wrongly indicates that the XYZ virus is present in five per cent of the cases in which the person does not have the virus.

What is the probability that an individual testing positive actually has the XYZ virus?

**Answer **

Most people say 95 % … but the answer is 2%.

If one in 1,000 people has the disease, 999 don’t.

But with a five per cent false-positive rate, the test will show that almost 50 of them are infected (5% X 999 = 49.95 = approx. 50).

Of 51 patients testing positive, only one will actually be infected.

And, 1 divided by 51 is about 2%

“The math here isn’t especially hard. But thinking the problem through is tricky.”

*Source
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October 16, 2014 at 10:40 am |

Excuse me Prof. Homa, but giving the right answer to the question is not a matter of logic, but one of knowing the right formula to calculate a false positive. FP / (FP + TN)