A rare metal is found in 1/1000 soil samples taken in the field. You develop a field test that is 90% accurate whether testing positive or negative for the metal. If the field team only brings back samples that test positive in the field, what is the probability that a sample brought back to the lab contains the rare metal?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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A rare metal is found in 1/1000 soil samples taken in the field. You develop a field test that is 90% accurate whether testing positive or negative for the metal.

If the field team only brings back samples that test positive in the field, what is the probability that a sample brought back to the lab contains the rare metal?

 

Your answer should be expressed with 3 significant digits of accuracy.

Expert Solution
Step 1

Given information:

P(Metal found)=11000=0.001P(No metal found)=1-P(Finding the metal)=1-0.001=0.999

PPositiveMetal=0.90PNegativeMetal=1-PPositiveMetalPNegativeMetal=1-0.90=0.10

PNegativeNo metal=0.90PPositiveNo Metal=1-PNegativeNo metalPPositiveNo Metal=1-0.90=0.10

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