Components of a certain type are shipped to a supplier in batches of ten. Suppos

Question

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 47% of all such batches contain no defective components, 28% contain one defective component, and 25% contain two defective components. Two components from a batch are randomly selected and tested. What are the probabilities associated with 0, 1, and 2 defective components being in the batch under each of the following conditions?

a) Neither tested component is defective.

1) no defective components

2) one defective component

3) two defective components

b) One of the two tested components is defective.

1) no defective components

2) one defective component

3) two defective components

Explanation / Answer

a) Neither tested component is defective. So, it could have come from any of the batches.

Thus, sample space = 100%

1) P (no defective components) = 47% / (47% + 28% + 25%)

= 0.47

2) P (one defective component) = 28% / (47% + 28% + 25%)

= 0.28

3) P (two defective components) = 25% / (47% + 28% + 25%)

= 0.25

b) One of the two tested components is defective.. Thus, it must have come in the batches with atleast one defectives or two defectives.

Thus, sample space = (28% + 25%) = 53%

1) P (no defective components) = 0 / 53%

= 0

2) P (one defective component) = 28 / (28% + 25%) = 28 / 53

= 0.5283

3) P (two defective components) = 25 / (28% + 25%) = 25 / 53

= 0.4717

Hope this helps.

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