Question

Finding Complements. In Exercises 5–8, find the indicated complements.

LOL A U.S. Cellular survey of smartphone users showed that 26% of respondents answered “yes” when asked if abbreviations (such as LOL) are annoying when texting. What is the probability of randomly selecting a smartphone user and getting a response other than “yes”?

Short answer

The probability of selecting a user who has answered other than “yes” is equal to 0.74.

Step-by-step solution

Given information

In a survey, 26% of the respondents answered “yes” to a question.

The question inquired, “if abbreviations (such as LOL) are annoying when texting.”

Define complementary events

If A stands for the occurrence of an event, then denotes the event that A does not occur. In that case, A and arecomplementary events.

Also,

$P\left(A\right)+P\left(\overline{A}\right)=1$

Compute the probability of a complementary event

Let A be the event of selecting a user who answered “yes” to the question.

Then, $\overline{A}$is the event of selecting a user who did not answer “yes.”

The percentages are divided by 100 to obtain the probability value.

It is calculated as shown below:

$$\begin{gathered} P\left(\overline{A}\right)=1-P\left(A\right) \\ =1-\frac{26}{100} \\ =\frac{74}{100} \\ =0.74 \end{gathered}$$

Therefore, the probability of selecting a respondent who answered other than “yes” is equal to 0.74.