anonymous
  • anonymous
MEDAL GIVEN PLEASE HELP A local television station sends out questionnaires to determine if viewers would rather see a documentary, an interview show, or reruns of a game show. There were 300 responses with the following results: 90 were interested in an interview show and a documentary, but not reruns. 12 were interested in an interview show and reruns but not a documentary 42 were interested in reruns but not an interview show. 72 were interested in an interview show but not a documentary. 30 were interested in a documentary and reruns. 18 were interested in an interview show and reruns. 24 were interested in none of the three. How many are interested in exactly one kind of show?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@ParthKohli
ParthKohli
  • ParthKohli
looks like a direct application of inclusion and exclusion
anonymous
  • anonymous
whats that?

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More answers

ParthKohli
  • ParthKohli
the inclusion-exclusion principle? the principle says:\[|A \cup B \cup C| = |A|+|B|+|C|-|A \cap B| - |B\cap C| - |A\cap C|+|A\cap B \cap C|\]
ParthKohli
  • ParthKohli
this is very clear with a venn diagram
anonymous
  • anonymous
I could use that equation to solve?
ParthKohli
  • ParthKohli
Yes you definitely can.
anonymous
  • anonymous
what if I have A B C AND D
ParthKohli
  • ParthKohli
Well actually I just read the question again, and it is a little twisted.
anonymous
  • anonymous
can you help me construct it?
FortyTheRapper
  • FortyTheRapper
The keyword in each of those scenarios is "And" And usually means more than one, right?
ParthKohli
  • ParthKohli
OK, start out with a nice little Venn diagram.
anonymous
  • anonymous
should I draw one on here?
ParthKohli
  • ParthKohli
|dw:1449953609476:dw|
anonymous
  • anonymous
|dw:1449953579261:dw|
anonymous
  • anonymous
|dw:1449953669857:dw|
anonymous
  • anonymous
was I doing it right?
ParthKohli
  • ParthKohli
yes, go on
anonymous
  • anonymous
|dw:1449953864120:dw|
anonymous
  • anonymous
do I do 72-18?
ParthKohli
  • ParthKohli
|dw:1449954053483:dw|
ParthKohli
  • ParthKohli
first, we remove 24 people from 300 then we remove 30+12 then we remove 90
ParthKohli
  • ParthKohli
i wonder if that is it
anonymous
  • anonymous
I don't really understand that the answer is supposed to be 144
ParthKohli
  • ParthKohli
oh wow! 300 - 30 - 12 - 24 - 90 = 144
ParthKohli
  • ParthKohli
wait, is that the given answer or...?
anonymous
  • anonymous
yeah I'm doing a study guide and my teacher gave us the asnwers to the study guide
ParthKohli
  • ParthKohli
so 144 it is, then? if it is, I'll explain you how
anonymous
  • anonymous
yes its 144 and yes please explain
ParthKohli
  • ParthKohli
ok first of all you were giving an overwhelming amount of information you didn't need, so don't be too worried about it let's recap: we need to remove this thing from the 300 people.|dw:1449954570392:dw|
anonymous
  • anonymous
okay I understand that part
ParthKohli
  • ParthKohli
for this region there are 24 people|dw:1449954628128:dw|
anonymous
  • anonymous
yes
ParthKohli
  • ParthKohli
for this region, there are 90 people|dw:1449954655040:dw|
ParthKohli
  • ParthKohli
for this region, there are 30 people|dw:1449954680451:dw|
ParthKohli
  • ParthKohli
for this region, there are 12 people|dw:1449954707748:dw|
anonymous
  • anonymous
wait
ParthKohli
  • ParthKohli
if you superimpose all regions you will get this|dw:1449954749084:dw|
anonymous
  • anonymous
why is there 30 in the middle?
ParthKohli
  • ParthKohli
30 were interested in a documentary and reruns.
anonymous
  • anonymous
oh cause you drew lines in the middle too
ParthKohli
  • ParthKohli
sorry about that so if you go through the problem and cross-check all the information with the Venn diagram, you'll see that this wasn't as hard as the inclusion-exclusion principle. all we needed was the ability to identify the regions that we could consider so that they add up the ultimate set.
anonymous
  • anonymous
oh because they wanted one kind of show so you had to exclude all the others that didn't include one type of show?
ParthKohli
  • ParthKohli
yeah exactly. I think we could have taken other paths to solve this problem but none of them would have been this easy. that's the beauty of mathematics.

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