Question

A water well is to be drilled in the desert where the soil is either rock, clay or sande. The probability of rock is P(R)=0.53. The clay probability is P(C)=0.21. The sand probability is P(S)=0.26. If it is rock, a geological test gives a positive result with 35% accuracy. If it is clay, a geological test gives a positive result with 48% accuracy.The test gives a positive result with 75% accuracy for sand. Given the test is positive, what is the probability that soil is sand, P(sand l positive)?

Answer 1

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%.