Question

Social Networking Based on data from the Pew Internet Project, 74% of adult Internet users use social networking sites. If two adult Internet users are randomly selected, what is the probability that they both use social networking sites?

Short answer

The probability that both randomly selected adults use social networking sites is 0.548.

Step-by-step solution

Given information

Seventy four percent of adult internet users use social networking sites.

Two adults are randomly selected from the population.

Describe the probability of any event

The mathematical formula for measuring the probability of an event Eis:

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

The measure gives the likelihood of an event.

When two independent events take place simultaneously, the probability of co-occurrence is represented as $P\left(E\text{and}F\right)=P\left(E\right)\times P\left(F\right)$for any arbitrary event F .

Define events and associated probability

Let E be the event of selecting the first adult and F be the event of selecting the second adult who uses social networking sites.

Assume that the probability is the same for all adults, and any of the two are independent.

Thus, the probability that both adults use social networking sites is calculated as:

$$\begin{gathered} P\left(E\text{and}F\right)=P\left(E\right)\times P\left(F\right) \\ =0.74\times 0.74 \\ =0.5476 \\ \approx 0.548 \end{gathered}$$

Therefore, the probability that both adults use social networking sites is 0.548.