We have three boxes. Box I contains 1,000 components, 1 out of 8 of which are de

Question

We have three boxes. Box I contains 1,000 components, 1 out of 8 of which are defective. Box II contains 800 components, 3 out of 8 of which are defective. Box III contains 3,200 components, 1 out of 4 of which are defective. We ?rst select at random one of the boxes and then remove at random a single component.

a) What is the probability that the selected component is defective?

b) We examine the component selected above and we ?nd it defective. On the basis of this evidence, determine the probability that it came from Box II.

Explanation / Answer

a.) 24.5% defective rate
First determine the chance of picking from each box:
125+300+800 defective parts out of 1000+800+3200 total parts = 1225/5000 = 24.5%

b.) 24.49% that it came from Box 2
300 / 1225 total defective parts = 24.49%

CHart provided below

# Components Failure Rate # of Defective Parts Box 1 1000 0.125 125 10.20% Box 2 800 0.375 300 24.49% Box 3 3200 0.25 800 65.31% Total 5000 0.245 1225

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