Question

A water well is being drilled in the desert where soil is either rock, clay, or sand. Probability of rock P(R) = 0.42, probability of clay P(C) = 0.34, and probability of sand P(S) =0.24. A geological test gives positive results with 40% accuracy in rock, 50% accuracy with clay, and 80% accuracy in sand. Given the test is positive, what is the probability that the soil is rock, P(Rock|positive)? Use Bayes’ rule.

Answer 1

The probality is 19.5

Answer 2

We are asked to solve for:

P (sand | positive)

So, we solve this by:

P (sand | positive) = P (sand)  x P (positive for sand)

P (sand | positive) = 0.26 (0.75)

P (sand | positive) = 0.195

The probability is 0.195 or 19.5%.