Question

Sharing music online $(5.2,5.3)$ A sample survey reports that 29% of Internet users download music files online, $21\%$ share music files from their computers, and $12\%$ both download and share music.

a. Make a two-way table that displays this information.

b. What percent of Internet users neither download nor share music files?

c. Given that an Internet user downloads music files online, what is the probability that this person also shares music files?

Short answer

Part (c) $41.38\%$

Part (b) $62\%$

Part (a)

	Download online	Do not download	Total
Share music files	12%	9%	21%
Do not share music files	17%	62%	79%
Total	29%	71%	100%

Step-by-step solution

Part (a) Step 1: Given information

$9$ percent of Internet users download music files from the internet, $21\%$ share music files from their PCs, and $12\%$ download and share music simultaneously.

Part (a) Step 2: Explanation

The fraction of internet users who download music files from the internet and distribute music files from their computers is of relevance here. $29$percent of internet users download music files from the internet, while $21\%$exchange music files and $12\%$do both. They also understand that the table must comprise $100$percent of all internet users.

Using the known row/column, the remaining percentages may be calculated.

	Download online
Share music file	12%	21-12=9%	21%
Do not share music files	29-12=17%	71-9=62%	100-21=79%
Total	29%	100-29=71%	100%

Part (b) Step 1: Explanation

From the previous solution

	Download online	Do not download online	Total
Share music files	12%	9%	21%
Do not share music files	17%	62%	79%
Total	29%	71%	100%

The percentage of internet users who do not download or share music files is provided in the table above in the row "do not share music files" and column "do not download online," which is $62$percent.

Part (c) Step 1: Explanation

From the previous solution

	Download online	Do not download online	Total
Share music files	12%	9%	21%
Do not share music files	17%	62%	79%
Total	29%	71%	100%

$$\begin{gathered} P(downloadonline)=29\%=0.29 \\ P(sharemusicfileanddownloadonline)=12\%=0.12 \\ P\left(B\right|A)=\frac{P(A\cap B)}{P\left(A\right)} \\ =\frac{P(sharemusicfileanddownloadonline)}{P(downloadonline)} \\ =\frac{0.12}{0.29} \\ =0.4138 \\ =41.38\% \end{gathered}$$