Chapter 5, Problem 105CRE

Simulating Guessing on a Multiple-Choice Test Suppose a student takes a 10-question multiple-choice quiz, and for each question on the quiz there are five possible options. Only one option is correct. Now suppose the student, who did not study, guesses at random for each question. A passing grade is 3 (or more) correct. We wish to design a simulation to find the probability that a student who is guessing can pass the exam.

a. In this simulation, the random action consists of a student guessing on a question that has five

possible answers. We will simulate this by selecting a single digit from the random number

table given in this exercise.

In this table, we will let 0 and 1 represent correct answers, and 2 through 9 will represent

incorrect answers. Explain why this is a correct approach for the exam questions with five

possible answers.

(This completes the first two steps of the simulation summary given in Section 5.4.)

b. A trial, in this simulation, consists of picking 10 digits in a row. Each digit represents one guess on a question on the exam. Write the sequence of numbers from the first trial. Also translate this to correct and incorrect answers by writing R for right and W for wrong. (This completes step 4.)

c. We are interested in knowing whether there were 3 or more correct answers chosen. Did this occur in the first trial? (This completes step 5.)

d. Perform a second simulation of the student taking this 10-question quiz by guessing randomly. Use the second line of the table given. What score did your student get? Did the event of interest occur this time?

e. Repeat the trial twice more, using lines 3 and 4 of the table. For each trial, write the score and whether or not the event occurred.

f. On the basis of these four trials, what is the empirical probability of passing the exam by guessing?