On an online math assignment, a student is allowed to submit an unlimited number of answers before moving on to the next problem. The problem is a free response problem, and the student believes that his guessed answer is correct about 8% of the time. (There are so many possible guesses that he thinks this percent stays the same every time). Under these assumptions, let M be the number of attempts he needs to submit a di erent random guessed answer until he gets the correct answer.
(a) What are the distribution and parameters of M?
(b) How many guesses should he expect to make on one problem if he refuses to learn the material?
(c) What is the probability it takes him at least 20 tries to get the problem correct?
(d) If there are 10 homework problems of a similar nature on this assignment, and he uses the same random technique with all of the problems, what is the probability that 4 of the 10 problems take at least 20 tries to get the problem right? What distribution and parameters are you using?
(e) If each homework problem takes 2 minutes to read (once) and 30 seconds for each random entry attempt, what is the expected time it will take to nish 1 problem?
(f) What is the expected time it will take to finish the homework assignment (all 10 problems)?