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) ?

Question

Kamren Watts

Mathematics

20 June, 21:29

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) ?

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Answers (1)

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Tatiana Wiley · 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%.