Unobtanium (Solution)

This is a classic bayesian puzzle. Out of every 100 rocks, 1 of them will have unobtanium and 99 will not. Your friend’s detector will give you a false positive on 10% of the 99, which is 9.9 rocks. Let’s just round that to 10. The detector will also give a (true) positive result on the 1 rock that does have unobtanium.

So the detector will give a positive result on 11 rocks: 10 false positives + 1 true positives. So the chance the rock has unobtanium given a positive is 1/11 ~= 9%.

If a rock with unobtanium is worth $1000 (and it’s worthless otherwise), and it’s 9% to have unobtanium, then the value of the rock is about $90 dollars (closer to $92 if you do all the math correctly). So definitely not worth paying $200.