Brandon S.

# problem solving

of 300 students, 110 are in the chorus and 150 are in the band.  Of these students, 50 are in both chorus and the band.  How many students are neither in the chorus nor the band?

## 2 Answers By Expert Tutors

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Michael D.

The reasoning is sound but the arthmetic is flawed: 300 - ( 110 + 150 - 50) = 300 - 210 = 90.

This problem can be also be pictorially demonstrated using Venn diagrams where there are 4 regions: Chorus & Band = 50, Chorus and Not Band = 110 - 50 = 60; Not Chorus and Band = 150 - 50 = 100 then sum across the three mutually exclusive regions to obtain 210 that is in either chorus, band or both. Thus the fourth region Not Chorus and Not Band = 300 - 210 = 90. This problem is essential understanding for students who will eventually take statistics and probability.
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05/22/14

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