Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of the components are defect-free. Components are independently selected and tested one by one. Let y denote the number of components that must be tested until a defect-free component is obtained.

a. What is the smallest possible y value, and what outcome corresponds to this y value? What is the second smallest y value, and what is the corresponding outcome?

b. What is the set of all possible y values?

c. Calculate the probability of each of the five smallest y values. (You should see a pattern that leads to a simple formula for p( y), the probability distribution of y.)