Chapter 4, Problem 1CQQ

Standard Tests Standard tests, such as the SAT or ACT or MCAT, tend to make extensive use of multiple-choice questions because they are easy to grade using software. If one such multiple choice question has possible correct answers of a, b, c, d, e, what is the probability of a wrong answer if the answer is a random guess?

To determine

To obtain: The probability of selecting a wrong answer if the answer is a random guess.

Answer to Problem 1CQQ

The probability of selecting a wrong answer if the answer is a random guess is 0.8.

Explanation of Solution

Given info:

From the given information, ‘Standard tests’ uses multiple choice questions as it can be graded using a software. In a multiple-choice question, possible correct answers are ‘a, b, c, d, e’ .

Calculation:

Let event A denote the randomly selected answer is a correct answer.

The formula for probability of event A is,

$P\left(A\right)=\frac{\text{Number of ways event }A\text{ occurs}}{\text{Number of simple events}}$

Substitute 1 for ‘Number of ways of event A occurs’ and 5 for ‘Number of simple events’

$\begin{array}{c}P\left(A\right)=\frac{1}{5}\\ =0.2\end{array}$

The formula for probability of complement of event A is, $P\left(\overline{A}\right)=1-P\left(A\right)$

Substitute 0.2 for $P\left(A\right)$,

$\begin{array}{c}P\left(\overline{A}\right)=1-P\left(A\right)\\ =1-0.2\\ =0.8\end{array}$

Thus, the probability of selecting a wrong answer, if the answer is a random guess is 0.8.

Interpretation:

There is a 0.8 probability of selecting a wrong answer if the answer is a random guess.