Math Problem Statement
A computer manufacturer uses chips from three sources. Chips from sources A, B and C are defective with probabilities 0.005, 0.001 and 0.01, respectively. The proportions of chips from A, B and C are 0.5, 0.1 and 0.4 respectively. If a randomly selected chip is found to be defective, find (a) the probability that the chips are from A. (b) the probability that the chips are from B. (c) the probability that the chips are from
Solution
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Math Problem Analysis
Mathematical Concepts
Probability
Conditional Probability
Bayes' Theorem
Formulas
P(A|D) = (P(D|A) * P(A)) / P(D)
P(D) = P(D|A) * P(A) + P(D|B) * P(B) + P(D|C) * P(C)
Theorems
Bayes' Theorem
Law of Total Probability
Suitable Grade Level
Grades 10-12
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