2.13 On a large college campus, the students are able to get free copies of the

Question

2.13 On a large college campus, the students are able to get free copies of the school newspaper, the local newspaper, and a national paper. Eighty-two percent of the students read at least one of the papers, 42% read only the school newspaper, 18% read only the local paper, 6% read only the national paper, and 1% read all three papers. Fifty-two percent read the school newspaper, and 5% read the school and national newspapers. A randomly selected student is asked whether he or she reads the school, local, or national paper. Express each of the following events in set notation and find the percentage of students represented by each. a The student does not read any paper. b The student reads the local paper. c The student reads exactly two papers d The student reads at least two papers

Explanation / Answer

Answer to question in detail as follows:

A. 82% read alteast 1 newpaper

So, 18% will not read any newspaper

C. 42, 18 and 6 read only school ,only local and only national paper

1% reads all

Therefore, people who read 2 newspaper, is 82 - (42+18+6) -1 = 15%

D. Alteast 2 newspaper = 2newspaper + 3 newspaper = 15+1 = 16%

B. Only school and national is 5%-1% =4%

Since, 52% read school newpaper, 52-42-1 = 9% read both

So, % students reading local paper = Only local + all 3+ only(local+national) + only(local+school)

= Only local + all 3+ (Alteast 2 - all 3 - national+school)

= 18% + 1% + (16-1%-(5%-1%)) = 30%

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