About Venn Diagrams, i don't get how they work...?

Question

In a class of 50 students, 18 take Chorus, 26 take Band, and 2 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?

The answer is 16: chorus, 24 band, and 2 neither. but the total is 42. but before, there was 18 chorus and 26 band. That's 44 people. What happened to the 2 people??????

i am so confused.

Answer 1

Draw two boxes, circles, shapes, whichever is your fancy. First you put 2 in the middle, overlapping area, this is who you know are in both. Next, subtract 2 from chorus, 16, this is the chorus total not also in band. Then, subtract 2 from band, 24, this is the band members not in chorus also. 24+2+16 which is 42. The 2 are in both band and chorus.

Answer 2

What? There should be 8 neither: 18 in chorus + 24 in band that are not in chorus (subtract the two that are in both classes, since we've already counted them), which gives us 42 people, so there should be 8 in neither class, not 2. I suspect the original answer was 16 in ONLY chorus, 24 in ONLY band, and 2 in BOTH classes (again, giving 42), and that it went on to say that that implied that 8 are in neither class.

The reason why the totals are different is because in the second accounting, each person is counted only once. Whereas, if you simply add the number of people in the chorus to the number of people in band, you are actually counting 2 people twice. The following simplified diagram will help:

People in group A: {Alice, Eve}
People in group B: {Bob, Eve}
People in both groups: {Eve}

2 people in group A + 2 people in group B is 4 people. But you only have three people. If you simply add the numbers together, you are counting {Alice, Bob, Eve, Eve} even though Eve only needs to be counted once.

That help?

Answer 3

Venn Diagrams are quite simple- they are two circles. On one side you would have 'Chorus' and the other 'Band'. You would have Chorus=16 people (put that in the circle) and Band=24 people (put that in the 'Band' circle). Now those two circles overlap in the middle or 'both' category. so you have 2 in the middle. Now you have 42 people doing something (Band/Chorus/Both). So that leaves 8 people out of the 50 students not enrolled in something. It is 50-42 basically. Answer being 8.

Answer 4

The two people skipped school that day....

Actually, here is the deal.....

18 take chorus and 2 take chorus & band = 20 chorus takers.

26 take band and 2 take chorus & band = 28 band takers

50-20-28 = 2 neither

Answer 5

neither do I?