hen a new machine is functioning properly, only 6% of the items produced are def

Question

hen a new machine is functioning properly, only 6% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.

a. Using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.

Choose the Correct option from the above tree diagrams:
Select1234Item 1

b. How many experimental outcomes result in exactly one defect being found?

c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).

hen a new machine is functioning properly, only 6% of the items produced are defective. Assume that we will randomly select two parts produced on the machine and that we are interested in the number of defective parts found.

a. Using the Figure 5.3, select a tree diagram that shows this problem as a two-trial experiment. Here D: defective; G: not defective.

Choose the Correct option from the above tree diagrams:
Select1234Item 1

b. How many experimental outcomes result in exactly one defect being found?

c. Compute the probabilities associated with finding no defects, exactly one defect, and two defects (to 4 decimals).

Explanation / Answer

a) The correct answer is the second diagram. It gives correct no. of defects against D,D and G,D etc.

b) Two outcomes ( D,G) and (G,D) result in exactly one defect.

c) P( no defect ) = 0.94*0.94 = 0.8836

P( 1 defect) = 2* 0.06*0.94 = 0.1128

P( 2 defect) = 0.06*0.06 = 0.0036

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