Question

Components of a certain type are shipped to a supplier in batches of ten. Suppose that 49% of all such batches contain no defective components, 27% contain one defective component, and 24% 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? (Round your answers to four decimal places.)

(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 the three different types of batches.]

no defective components
one defective component
two defective components

Answer 1

a)

	a	b	a*b	ab/Σab
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
		Σab =	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