BSEE and MSEE with 8 years of heavy math and the fact that I still have to read the solution slowly and not really get it scares the bejeezers out of me.
If you have any kind of test that seems relatively accurate (5% failure rate), 1 in every 20 tests will be identified as a positive candidate no matter the actual incidence rate. When applied over a huge population the number of positive candidates is going to also be huge. Since the incidence rate in this scenario is so low (1/1000) the odds of a true positive selected from the positive candidates is also very low.
This is a little surprising to me. I was required to take a probability class for my BS in electrical engineering, and a version of this problem was a homework question.
Funny you should call this out: As an undergrad I got to choose between a prob & statistics path and a complex math / advance calc path. I took the complex math path. However, I was required to take a semester on engineering methods that touched on statistics, but that was part of one semester. As a grad student, I went down the numerical methods path for parallel computing. Not as many classes as undergrad, but still.