Statistics problem dealing with attendance

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SUMMARY

The discussion centers on a statistics problem involving attendance at three concerts: Pep Band, Country Sizzle, and Blue Mood. Key attendance figures include 48 for Pep Band, 36 for Country Sizzle, and 60 for Blue Mood, with overlaps of 12, 20, and 16 for pairs of concerts. The correct number of students who attended all three concerts is determined to be 4. Utilizing a Venn diagram is recommended for visualizing the intersections and solving the problem accurately.

PREREQUISITES
  • Understanding of basic set theory and Venn diagrams
  • Familiarity with the principle of inclusion-exclusion in statistics
  • Ability to perform basic arithmetic operations with sets
  • Knowledge of how to interpret and analyze attendance data
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  • Study the principle of inclusion-exclusion in detail
  • Practice creating and interpreting Venn diagrams for various set problems
  • Learn about combinatorial counting techniques
  • Explore real-world applications of set theory in statistics
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Students studying statistics, educators teaching set theory, and anyone interested in solving combinatorial problems involving multiple sets.

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One hundred students attended at least one of three concerts: Pep Band, Country Sizzle, and Blue Mood. 48 heard the Pep Band concert. 36 heard the Country Sizzle concert. 60 heard the Blue Mood concert. 12 heard the Pep Band and Country Sizzle concerts. 20 heard the Country Sizzle and Blue Mood concerts. 16 heard the Pep Band and Blue Mood concerts. How many attended all three concerts?

Ok So I broke it down. The max number of people that could attend all three would be 12 since that is how many attened the Pep Band and Country Sizzle which is the least number. I do not really know how to proceed on this problem. If I had to guess my answer would be 4 attended all 3 because there is a difference of 4 between 12, 16, and 20. Also when adding those together you get 48. Then adding the others together and subtracting 100 you get 44, once again a difference of 4. But I am faily certain that is not the correct way to approach the problem.
 
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Well, I have no idea what your reasoning is but 4 is the correct answer. Draw a Venn diagram to help you visualize it, and add and subtract to find the intersection of the 3 concerts.
 

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