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Imagine a mine where exactly 1% of the rocks contain a small diamond embedded within them worth exactly
$1,000. You have a diamond detector that always beeps if a diamond is embedded within a rock. If there is
no diamond within the rock, 10% of the time the detector will detect a false positive (that is to say it
will beep even though no diamond is present). The owner of the mine allows you to use your device on one
of the rocks. You pick up a random, unmarked rock and the detector beeps. The owner offers to sell you
the rock for $200. If the rock contains a diamond, it's worth $1,000; if it doesn't, it's worthless.
Should you buy the rock?
