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Answer :
Final answer:
A total of 62 students read at least one magazine, while 38 students read none of the magazines. This conclusion is reached using the principle of inclusion-exclusion. The calculation considers overlaps among the different magazines.
Explanation:
Understanding Magazine Readership Among College Students
To find the number of students who read at least one magazine and those who read none, we can use the principle of inclusion-exclusion.
a. Students who read at least one magazine
Let:
- A = students who read Time Magazine
- B = students who read a Newspaper
- C = students who read US News
From the survey, we have:
- |A| = 40% of 100 = 40 students
- |B| = 30% of 100 = 30 students
- |C| = 25% of 100 = 25 students
The numbers of students reading two magazines are:
- |A ∩ B| = 15% of 100 = 15 students
- |A ∩ C| = 12% of 100 = 12 students
- |B ∩ C| = 10% of 100 = 10 students
And the number of students reading all three magazines:
- |A ∩ B ∩ C| = 4% of 100 = 4 students
Using the inclusion-exclusion principle, the formula to find the number of students who read at least one magazine is:
|A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C|
Substituting the values:
|A ∪ B ∪ C| = 40 + 30 + 25 - 15 - 12 - 10 + 4 = 62
b. Students who read none of the magazines
To find the number of students who read none of the magazines, subtract the number of students who read at least one magazine from the total number of students:
Students reading none = Total students - Students reading at least one = 100 - 62 = 38 students
In summary, 62 students read at least one magazine, while 38 students read none of these three magazines.
Learn more about Magazine Readership here:
https://brainly.com/question/52045773
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