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.

Question

Rigoberto

Mathematics

15 January, 01:45

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.

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Answers (2)

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Marilyn Berg · 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%.

Aubree Montes · Answer 2

Aubree Montes 15 January, 02:05

0

The probality is 19.5