Use Bayes' Rule to Find the Indicated Probability

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