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 8 out of 10 chances of passing on any one attempt by luck. What is Elaine's likelihood of passing on at least one of the 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. Elaine will of course stop taking the exam as soon as she passes.
(b) Simulate 50 repetitions. What is your estimate of Elaine's likelihood of passing the course?
(c) Do you think the assumption that Elaine's likelihood of passing the exam is the same on each trial is realistic? Why?
No, learning usually occurs in taking an exam.
Yes, the test should be on the same knowledge each time.
No, she will have studied more before the first test.
Yes, Elaine is still the same person from test to test.