Use Bayes' Rule to Find the Indicated Probability

question 13

Multiple Choice

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(rock | positive) ?

• A)P(rock | positive)= 0.209
• B)P(rock | positive)= 0.405
• C)P(rock | positive)= 0.53
• D)P(rock | positive)= 0.385

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