19.18 Repeating an exam. Elaine is enrolled in a self-paced course that allows three attempts to pass an examination on the material. She does not study and has probability 2-in-10 of passing on any one attempt by luck. What is Elaine’s probability of passing in three attempts? (Assume the attempts are independent because she takes a different examination on each attempt.)
(a) Explain how you would use random digits to simulate one attempt at the exam.
(b) Elaine will stop taking the exam as soon as she passes. (This is much like Examples 4.) Simulate 50 repetitions, starting at line 120 of Table A. What is your estimate of Elaine’s probability of passing the exam?
(c) Do you think the assumption that Elaine’s probability of passing the exam is the same on each trial is realistic? Why?