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

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Basic Math

Components of a certain type are shipped to a supplier inbatches of ten. Suppose that 49% of all such batches contain nodefective components, 27% contain one defective component, and 24%contain two defective components. Two components from a batch arerandomly selected and tested. What are the probabilities associatedwith 0, 1, and 2 defective components being in the batch under eachof the following conditions? (Round your answers to four decimalplaces.)

(a) Neither tested component is defective.

no defective components:    
one defective component:    
two defective components:   


(b) One of the two tested components is defective. [Hint:Draw a tree diagram with three first-generation branches for thethree different types of batches.]

no defective components    
one defective component    
two defective components    

Answer & Explanation Solved by verified expert
4.2 Ratings (661 Votes)

a)

a b a*b ab/?ab
x P(x) P(no defect|x) P(x and no defect) P(x|no defect)
0 0.49 1.0000 0.4900 0.5729
1 0.27 0.8000 0.2160 0.2525
2 0.24 0.6222 0.1493 0.1746
?ab = 0.8553

from above:

P(no defective batch given no defective)=P(no defective batch and no defective)/P(no defective)=0.5729

P(one defective batch given no defective)=P(one defective batch and no defective)/P(no defective)=0.2525
P(two defective batch given no defective)=P(two defective batch and no defective)/P(no defective)=0.1746

b)

as above:

P(no defective batch given one defective)=P(no defective batch and one defective)/P(one defective)=0
P(one defective batch given one defective)=P(one defective batch and one defective)/P(one defective)=0.3876
P(two defective batch given one defective)=P(two defective batch and one defective)/P(one defective)=0.6124

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