I was a mathematician, and now work in finance (systematic trading). I've found a reasonable negative filter is A jar has 1000 coins, of which 999 are fair and 1 is double headed. Pick a coin at random, and toss it 10 times. Given that you see 10 heads, what is the probability that the next toss of that coin is also a head? That tests their ability to turn a problem into mathematics, and some very basic conditional p…
That's a nice filter. (Of course, I'm a former mathematician as well.) Here's how I think of it: - the prior odds that you picked the double-headed coin are 1/999. - after seeing ten heads, the posterior odds that you picked the double-headed coin are (2^10)/999 - let's approximate this as 1. (Bayes' theorem usually gets expressed in terms of probabilities, but it's so much simpler in terms of odds.) - so it's roughl…
http://yudkowsky.net/rational/bayes
Useful if you want to know (or need a good way to explain) what a posterior probability is and how it's different from a prior probability