Chapter 4, Problem 1CQQ

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.