Question

Myspace versus Facebook A recent survey suggests that $85\%$ of college students have posted a profile on Facebook, $54\%$use Myspace regularly, and $42\%$ do both. Suppose we select a college student at random.

(a) Assuming that there are $20$ million college students, make a two-way table for this chance process.

(b) Construct a Venn diagram to represent this setting.

(c) Consider the event that the randomly selected college student has posted a profile on at least one of these two sites. Write this event in symbolic form

using the two events of interest that you chose in (b).

(d) Find the probability of the event described in (c).

Explain your method.

Short answer

Part (a) The table is

Part (b) Venn diagram is

Part (c) Event is P(Facebook ∪ Myspace)

Part (d)$P(Facebook\cup Myspace)=0.97$

Step-by-step solution

Part (a) Step 1. Given Information

The following is a two-way table for the given problem:

Part (a) Step 2. Concept Used

A Venn diagram is a visual representation of relationships between things or limited groups of objects using circles. Circles that overlap have similar qualities to circles that do not overlap. Venn diagrams are graphic representations of the similarities and differences between two concepts.

Part (a)  Step 3. Explanation

85 percent of Facebook users are on the platform.

The percentage of Myspace users is 54 percent.

The percentage of people that use Facebook and Myspace is 42 percent.

There are 20 million college students in the United States.

As a result, the two-way table becomes,

Part (b) Step 1. Explanation

Venn diagram becomes

Part (c) Step 1. Explanation

College students are more likely to use Facebook or Myspace, or both. This can be expressed symbolically as, $P(Facebook\cup Myspace)$

Part (d) Step 1. Calculation

$Probability=\frac{Numberoffavorableoutcomes}{Totalpossibleoutcomes}$

Total number of possible outcomes $20,000,000$

Therefore, $$\begin{gathered} P(Facebook\cup Myspace)=\frac{8,600,000+8,400,000+2,400,000}{20,000,000} \\ P(Facebook\cup Myspace)=\frac{19,400,000}{20,000,000}=0.97 \end{gathered}$$