Math Problem Statement
A factory produces a certain type of output by three types of machines. The
respective daily production figures are Machine I: 3,000 units, Machine II: 2,500 units and Machine III: 4,500 units. = 800
Past experience shows that 1% of the output produced by Machine I is defective. The corresponding fraction of defectives for the other two machines are 1.2% and 2% respectively. An item is drawn at random from the day's production run and is found to be defective. What is the probability that it comes from the output of (a) Machine 1, (b) Machine II and (c) Machine III?
Solution
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Bayes' Theorem
Conditional Probability
Formulas
Total Probability: P(D) = P(D|I)*P(I) + P(D|II)*P(II) + P(D|III)*P(III)
Bayes' Theorem: P(I|D) = (P(D|I) * P(I)) / P(D)
Theorems
Bayes' Theorem
Law of Total Probability
Suitable Grade Level
Grades 10-12
Related Recommendation
Probability of Defective Products from Two Machines Using Bayes' Theorem
Bayes' Theorem: Probability of Defective Item Produced by Machine B
Probability of Defective Item from Machine A or B Using Bayes' Theorem
Calculate Probability of Defective Bolts Using Bayes' Theorem
Calculating the Probability of Defective Parts Using Bayes' Theorem