An water well is to be drilled in the desert where the soil is either rock, clay or sand. The

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 the soil is rock, P (rock | positive)?

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