Question

In Exercises 13–20, express the indicated degree of likelihood as a probability value between 0 and 1.

SAT Test When making a random guess for an answer to a multiple-choice question on an SAT test, the possible answers are a, b, c, d, e, so there is 1 chance in 5 of being correct.

Short answer

The probability of getting the correct answer in a multiple-choice question is 0.2.

Step-by-step solution

Given information

For a multiple-choice question, there are five options (a, b, c, d, e).

There are 1 in 5 chances of getting the correct answer.

Define probability

Probability is a number that tells the likelihood of the occurrence of an event.

It is computed using the formula

$P\left(A\right)=\frac{\text{Number}\text{of}\text{outcomes}\text{in}\text{which}\text{A}\text{is}\text{likely}\text{to}\text{occur}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Calculate the probability 

Here, the total number of answers for a multiple-choice question is five.

There is 1 in 5 chances to get the correct answer.

It means the number of correct answers is 1.

Considering that all the choices are equally likely to occur, the probability of getting the correct answer is

$$\begin{gathered} P\left(\text{correct}\text{choice}\right)=\frac{\text{Number}\text{of}\text{correct}\text{choices}}{\text{Total}\text{number}\text{of}\text{choices}} \\ =\frac{1}{5} \\ =0.2 \end{gathered}$$

Therefore, the probability of choosing the correct answer is 0.2.