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A survey of 100 college students who frequently read university language magazines revealed the following results:

- 40% read Time Magazine
- 30% read a Newspaper
- 25% read US News
- 15% read Time Magazine and a Newspaper
- 12% read Time Magazine and US News
- 10% read a Newspaper and US News
- 4% read all three magazines

How many of the students read:

a. At least one magazine?
b. None of these three magazines?

Answer :

Final answer:

A total of 62 students read at least one magazine, while 38 students read none of the three magazines surveyed.


Explanation:

Analyzing Magazine Readership Among College Students


To solve the problem of how many students read at least one magazine and how many read none, we can use the principles of set theory and the inclusion-exclusion principle.



Given Data



  • Total students surveyed: 100

  • Read Time Magazine (T): 40 students

  • Read Newspaper (N): 30 students

  • Read US News (U): 25 students

  • Read both Time Magazine and Newspaper (T ∩ N): 15 students

  • Read both Time Magazine and US News (T ∩ U): 12 students

  • Read both Newspaper and US News (N ∩ U): 10 students

  • Read all three magazines (T ∩ N ∩ U): 4 students



Using Inclusion-Exclusion Principle


The formula for at least one of the sets (magazines) is given by:


n(T ∪ N ∪ U) = n(T) + n(N) + n(U) - n(T ∩ N) - n(T ∩ U) - n(N ∩ U) + n(T ∩ N ∩ U)



Substituting the values:



  2. n(T) = 40

  4. n(N) = 30

  6. n(U) = 25

  8. n(T ∩ N) = 15

  10. n(T ∩ U) = 12

  12. n(N ∩ U) = 10

  14. n(T ∩ N ∩ U) = 4



Now plugging these values into the formula:


n(T ∪ N ∪ U) = 40 + 30 + 25 - 15 - 12 - 10 + 4 = 62



This means that 62 students read at least one magazine.



Calculating Students Who Read None


To find how many students read none of the magazines, we simply subtract the number of students who read at least one magazine from the total number of surveyed students:


100 (total students) - 62 (students who read at least one) = 38


Thus, 38 students read none of these three magazines.


Learn more about Magazines Readership here:

https://brainly.com/question/52045773


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