Question

In Exercises 25–32, find the probability and answer the questions. Social Networking In a Pew Research Center survey of Internet users, 3732 respondents say that they use social networking sites and 1380 respondents say that they do not use social networking sites. What is the probability that a randomly selected person does not use a social networking site? Does that result suggest that it is unlikely for someone to not use social networking sites

Short answer

The probability that a randomly selected respondent does not use social networking sites is equal to 0.270.

No, it is not unlikely for a person to not use social networking sites.

Step-by-step solution

Given information

In a survey, the number of respondents who use social networking sites is equal to 3732.

The number of respondents who do not use social networking sites is equal to 1380.

Probability

Theprobability of an event is the number of favorable results of an event upon the total number of results.

Mathematically,

$P\left(A\right)=\frac{\text{Number}\text{of}\text{favourable}\text{results}\text{of}\text{A}}{\text{Total}\text{number}\text{of}\text{results}}$

Calculating the probability value

The total number of respondents is the sum of the number of respondents who use social networking sites and who do not use social networking sites.

It is calculated as follows:

$$\begin{gathered} \text{Total}\text{number}\text{of}\text{respondents}=3732+1380 \\ =5512 \end{gathered}$$

The number of respondents who do not use social networking sites is 1380

Let A be the event of selecting a respondent who does not use social networking sites.

The probability of E is calculated as follows:

$$\begin{gathered} P\left(E\right)=\frac{\text{Number}\text{of}\text{favourable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}} \\ =\frac{1380}{5112} \\ =0.270 \end{gathered}$$

Therefore, the probability of selecting a respondent who does not use social networking sites is equal to 0.270.

Examining the likelihood

It can be said that there is a 27% chance for a random respondent not to use social networking sites.

In other words, out of 100 respondents, 27 of them are unlikely to use social networking sites.

As the probability value is considerable (greater than 0.05), it can be said that it is likely (not unlikely) for a person not to use social networking sites.