19.25 A multiple-choice exam. Matt has lots of experience taking multiple-choice exams without doing much studying. He is about to take a quiz that has 10 multiple-choice questions, each with four possible answers. Here is Matt’s personal probability model. He thinks that in 75% of questions he can eliminate one answer as obviously wrong; then he guesses from the remaining three. He then has probability 1-in-3 of guessing the right answer. For the other 25% of questions, he must guess from all four answers, with probability 1-in-4 of guessing correctly.
(a) Make a tree diagram for the outcome of a single question. Explain how to simulate Matt’s success or failure on one question.
(b) Questions are independent. To simulate the quiz, just simulate 10 questions. Matt needs to get at least five questions right to pass the quiz. You could find his probability of passing by simulating many tries at the quiz, but we ask you to simulate just one try. Did Matt pass this quiz?