30. When a new machine is functioning properly, only 3% 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. Describe the conditions under which this situation would be a binomial experiment.

b. Draw a tree diagram similar to Figure 5.3 showing this problem as a two-trial experiment.

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

d. Compute the probabilities associated with finding no defects, exactly one defect, and two defects.