Use Bayes' rule to find the indicated probability.
-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 soil is rock,P(sand | positive)?
A)P(sand | positive)= 0.405
B)P(sand | positive)= 0.385
C)P(sand | positive)= 0.26
D)P(sand | positive)= 0.209

Question

Quizplus · Accepted Answer

To find P(sand | positive), use Bayes' rule: P(sand | positive) = [P(positive | sand) * P(sand)] / P(positive). First, calculate P(positive) = P(positive | rock) * P(rock) + P(positive | clay) * P(clay) + P(positive | sand) * P(sand) = 0.35 * 0.53 + 0.48 * 0.21 + 0.75 * 0.26 = 0.1855 + 0.1008 + 0.195 = 0.4813. Then, P(sand | positive) = (0.75 * 0.26) / 0.4813 = 0.195 / 0.4813 ≈ 0.405.

Use Bayes' Rule to Find the Indicated Probability