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

Question

Quizplus · Accepted Answer

P(rock | positive) = P(positive | rock) * P(rock) / P(positive)P(positive | rock) = 0.35P(rock) = 0.53P(positive) = P(positive | rock) * P(rock) + P(positive | clay) * P(clay) + P(positive | sand) * P(sand)P(positive | clay) = 0.48P(clay) = 0.21P(positive | sand) = 0.75P(sand) = 0.26P(positive) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26 = 0.462P(rock | positive) = 0.35 * 0.53 / 0.462 = 0.385

Use Bayes' Rule to Find the Indicated Probability