Question

A 10-question multiple-choice exam offers 5 choices for each question. Jason just guesses the answers, so he has probability $\frac{1}{5}$of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. What would be a proper way to use a table of random digits to do this?

a. One digit from the random digit table simulates one answer, with 5 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

b. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

c. One digit from the random digit table simulates one answer, with odd = correct and even = incorrect. Ten digits from the table simulate 10 answers.

d. One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect, ignoring repeats. Ten digits from the table simulate 10 answers.

e. Two digits from the random digit table simulate one answer, with 00 to 20 = correct and 21 to 99 = incorrect. Ten pairs of digits from the table simulate 10 answers.

Short answer

(b) One digit from the random digit table simulates one answer, with 0 or 1 = correct and all other digits = incorrect. Ten digits from the table simulate 10 answers.

Step-by-step solution

Given Information

Each question on a ten-question multiple-choice exam has five options.

Jason probability is$\frac{1}{5}$

Explanation for correct option

The likelihood of getting a correct answer must be calculated is $\frac{1}{5}$

because two of the ten potential numbers correspond to a correct response, implying a chance of$\frac{2}{10}=\frac{1}{5}$

Explanation for incorrect option

Option A is not match with because 5 of the 10 possible numbers correspond to a correct response, implying a chance of $\frac{5}{10}=\frac{1}{2}$instead of $\frac{1}{5}$

Option C is not match with because 5 of the 10 possible numbers correspond to a correct response, implying a chance of $\frac{5}{10}=\frac{1}{2}$instead of $\frac{1}{5}$

Option D is not match with because duplicates are not taken into account, the chances of getting a correct response are not the same for each question (while this probability should be constant).

Option E is not match with because 21 of the 100 possible pairs of digits correspond to a correct response, implying a chance of$\frac{21}{100}$instead of$\frac{1}{5}=\frac{20}{100}$