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(rock | positive)?
A)P(rock | positive)= 0.209
B)P(rock | positive)= 0.405
C)P(rock | positive)= 0.53
D)P(rock | positive)= 0.385

Question

Quizplus · Accepted Answer

To find P(rock | positive), use Bayes' rule: P(rock | positive) = [P(positive | rock) * P(rock)] / P(positive). Calculate P(positive) using the law of total probability: P(positive) = P(positive | rock) * P(rock) + P(positive | clay) * P(clay) + P(positive | sand) * P(sand). Substitute the given values and solve.

Use Bayes' Rule to Find the Indicated Probability