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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

Expert verified

Part (c) 41.38%

Part (b) 62%

Part (a)


Download onlineDo not downloadTotal
Share music files
12%9%21%
Do not share music files17%62%79%
Total29%71%100%

Step by step solution

01

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.

02

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. 29percent 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 100percent of all internet users.

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


Download online

Share music file12%21-12=9%
21%
Do not share music files29-12=17%71-9=62%100-21=79%
Total29%100-29=71%100%
03

Part (b) Step 1: Explanation

From the previous solution


Download onlineDo not download onlineTotal
Share music files12%9%21%
Do not share music files17%62%79%
Total29%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 62percent.

04

Part (c) Step 1: Explanation

From the previous solution


Download onlineDo not download onlineTotal
Share music files12%9%21%
Do not share music files17%62%79%
Total29%71%100%

P(downloadonline)=29%=0.29P(sharemusicfileanddownloadonline)=12%=0.12P(B|A)=P(A∩B)P(A)=P(sharemusicfileanddownloadonline)P(downloadonline)=0.120.29=0.4138=41.38%

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