Question

Asked Oct 25, 2019

In a manufacturing plant, three machines, A, B, and C, produce 38%, 33%, and 29%, respectively, of the total production. The company's quality-control department has determined that 2% of the items produced by machine A, 1.5% of the items produced by machine B, and 2% of the items produced by machine C are defective. If an item is selected at random and found to be defective, what is the probability that it was produced by machine B? (Round your answer to three decimal places.)

Step 1

Machine **A, B, C** produces **38%, 33%,** and **29%**.

**P(A) = 0.38 %, P (B) = 0.40** and** P(C) = 0.29%**

**D** denote the defective item.

**2%** of the items produced by machine** A** are defective, so **P(D/A) = 0.02**

**1.5%** of the items produced by machine **B** are defective, so **P(D/B) = 0.015**

**2%** of the items produced by machine **C** are defective, so **P(D/C) = 0.02**

To find the probability which is produced by machine **B**, or **P(B/D).**

** **

Now from the Bayes’ Theorem:

Step 2

put the given values i...

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