Sequential Searches: Proofreading, Russian Roulette, and the Incomplete q-Eulerian Polynomials Revisited

1. INTRODUCTION. So, you've read your fifty page manuscript a half dozen times and you continue to stumble across annoying typos. Is there any end in sight? Just how many more times do you need to read it before you're satisfied? For purposes of discussion, let's say that your manuscript originally contained 10 errors and that, because of fatigue and a certain level of impatience, the probability that you notice an error when staring right at it is only 1/10. Then the expected number of errors found is one after the first reading, 1.9 after the second reading, and so on. Several such results rounded to the nearest hundreth are shown in Table 1.