Chapter 7: Q. 4 (page 461)

A $10$ -question multiple-choice exam offers $5$ choices for each question. Jason just guesses the answers, so he has a probability $1 / 5$ of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following:
(a) One digit from the random digit table simulates one answer, with 5 $=$ right and all other digits $=$ wrong. Ten digits from the table simulate $10$ answers. (b) One digit from the random digit table simulates one answer, with 0 or 1 $=$ right and all other digits $=$ wrong. Ten digits from the table simulate $10$ answers.
(c) One digit from the random digit table simulates one answer, with odd $=$ right and even $=$ wrong. Ten digits from the table simulate $10$ answers.
(d) Two digits from the random digit table simulate one answer, with $00$ to $20$ $=$ right and $21$ to $99 =$ wrong. Ten pairs of digits from the table simulate $10$ answers.
(e) Two digits from the random digit table simulate one answer, with $00$ to $05 =$ right and $06$ to $99$ $=$ wrong. Ten pairs of digits from the table simulate $10$ answers.

Short Answer

Expert verified

One correct way to use the random digits is option (b) $0$ or $1 =$ right and all other digits $=$ wrong.

Step by step solution

Given information

A $10$ -question multiple-choice exam offers $5$ choices for each question.

He has a probability $1 / 5$ of getting any one answer correct.

Determine the number of correct answers he gets.

Explanation

The probability of a correct answer needs to be $1 / 5$

(a) Incorrect, because $5$ of the $10$ possible digits correspond with a right answer, which corresponds with a probability of $5 / 10 = 1 / 2$

(b) Correct, because $2$ of the $10$ possible digits correspond with a right answer, which corresponds with a probability of $2 / 10 = 1 / 5$

(c) Incorrect, because $5$ of the $10$ possible digits correspond with a right answer, which corresponds with a probability of $5 / 10 = 1 / 2$

(d) Incorrect, because repeats are being ignored and thus the probability of obtaining a correct answer is then not the same for each question (while this probability should be constant).

(e) Incorrect, because $21$ of the $100$ possible pairs of digits correspond with a right answer, which corresponds with a probability of $21 / 100$ instead of $1 / 5 = 20 / 100 .$