19.19 A better model for repeating an exam. A more realistic probability model for Elaine’s attempts to pass an exam in the previous exercise is as follows. On the first try she has probability 0.2 of passing. If she fails on the first try, her probability on the second try increases to 0.3 because she learned something from her first attempt. If she fails on two attempts, the probability of passing on a third attempt is 0.4. She will stop as soon as she passes. The course rules force her to stop after three attempts in any case.
(a) Make a tree diagram of Elaine’s progress. Notice that she has different probabilities of passing on each successive try.
(b) Explain how to simulate one repetition of Elaine’s tries at the exam.
(c) Simulate 50 repetitions and estimate the probability that Elaine eventually passes the exam. Use Table A, starting at line 130.