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# Mining Gold

## Question

Mining gold in a particular region is hard work.  The metal only appears in 1% of rocks in the mine. But your friend Old Joe created a detector he’s been perfecting for months and it is finally ready.  To your astonishment it always detect gold if gold is present.  Otherwise it will have a 90% accuracy rate in detecting that a particular rock does not have gold.  Working with Old Joe, You guys scan a large rock and determine that it gives a positive result.  In loading it up, Old Joe realizes that both of you can't fit into the vehicle.  He offers to sell his share to you for \$200.  You know that a rock of gold that size is worth easily  \$1000.  Is that a fair price?  Assume the vehicle remains with the proper owner.

## 4 answers to this question

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Spoiler

Yes. This is a question of Bayesian probability. The test results in a relatively large proportion of false positives. In fact, the majority of positives delivered by the test are actually false positives. Consider this case: say you scan a hundred rocks. Only 1%, or one rock, is actually gold. But your scan would result in ~9-10 false positives. That means you only have about a 10% chance that one particular positive rock actually has gold. Since the rock is worth \$1,000 with a 10% chance or \$0 with a 90% chance, the average value of the rock is just \$100. Hence, it's a better deal to take the guaranteed \$200 than the 10% chance at \$1,000.

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Posted (edited)

fb- Joe is trying to sell you his share. You are paying him the \$200... if you accept his offer.

A question

Who owns the car? If you take his offer and he owns the vehicle, you've got transportation issues. That said, I agree with flamebirde's reasoning so I guess either way, the odds are against you. Not owning the vehicle would just make it worse.

Edited by Thalia

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A different approach ...

Spoiler

It's going to cost a lot more to extract the gold from the rock. There are factors such as the form the gold is in (native or metallic alloy), the size of the gold-bearing phases (nuggety gold or submicroscopic occlusion) and the mode of occurrence of the "gold" grains in the host rock. So you need at least an applied mineralogist to determine the gold properties, an extraction metallurgist to devise the recovery method, and on top, the cost of the equipment and extraction process itself. That's what Joe must be able to afford. Therefore, if Joe offers me \$200. I'll certainly take it!

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21 hours ago, Thalia said:

fb- Joe is trying to sell you his share. You are paying him the \$200... if you accept his offer.

A question

Hide contents

Who owns the car? If you take his offer and he owns the vehicle, you've got transportation issues. That said, I agree with flamebirde's reasoning so I guess either way, the odds are against you. Not owning the vehicle would just make it worse.

whoops. In that case, I say refuse the offer. Assuming that the rest of the puzzle (i.e. the vehicle) is just story fluff and that the \$1000 price tag of the rock is after processing, my answer remains the same. His share isn't even worth \$100, let alone \$200.

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