Credit for this problem goes to Dennis Shasha, TED-Ed. Thanks!

Unobtanium

Mining unobtainium is hard work. The rare mineral appears in only 1% of rocks in the mine. But your friend Tricky Joe has something up his sleeve. The unobtainium detector he’s been perfecting for months is finally ready. The device never fails to detect unobtainium if any is present. Otherwise, it’s still highly reliable, returning accurate readings 90% of the time.

On his first day trying it out in the field, the device goes off, and Joe happily places the rock in his cart. As the two of you head back to camp where the ore can be examined, Joe makes you an offer: he’ll sell you the ore for just $200. You know that a piece of unobtanium that size would easily be worth $1000, but any other minerals would be effectively worthless.

Should you make the trade?

Solution