Components coming off an assembly line are either free of defects (S, for success) or defective (F, for failure). Suppose that 70% of all such 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 experimental outcome gives this y value? What is the second smallest y value, and what outcome gives rise to it?
b. What is the set of all possible y values?
c. Determine 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.