Use Bayes' Rule to Find the Indicated Probability

Use Bayes' rule to find the indicated probability.
-An water well is to be drilled in the desert where the soil is either rock,clay or sand.The probability of rock P(R) = 0.53.The clay probability is P(C) = 0.21.The sand probability is P(S) = 0.26.It if it rock,a geological test gives a positive result with 35% accuracy.If it is clay,this test gives a positive result with 48% accuracy.The test gives a 75% accuracy for sand.Given the test is positive,what is the probability that soil is rock,P(sand | positive) ?

A) P(sand | positive) = 0.405
B) P(sand | positive) = 0.385
C) P(sand | positive) = 0.26
D) P(sand | positive) = 0.209

Correct Answer:

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