1) A mining company has a test that can identify coal in a sample. We know...

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1) A mining company has a test that can identify coal in a sample. We know that 93% of a particular area that the mining company has leased contains no coal. Given a sample that has no coal is tested, it gives a result of no coal 97% of the time. Hoever, the test also incorrectly identifies a sample as not containing coal (given it actually does contain coal) 4.5% of the time. a) State each event. b) Write out the probabilities for this scenario using the probability notation taught in lectures and workshops. c) Find the probability of finding coal in a sample, given the test indicates that the sample contains coal.

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Answer 1

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This problem is based on the application of the Baye's theorem

e exem Coal → C Test NegahiveTN (Shouss c sence of oal No coal 193ツ·J TP T N TP () TN (37) r(Tp/c): , P(Tri|c): 4.r., gs. s:/ : P(TP (0-03) 00 97 ( 0) : O.O 0:09 475 Coal Tos imcli cot e coal 0.6832

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1) A mining company has a test that can identify coal in a sample. We know...

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