A probability question using a venn diagram. Please Help!

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EddyBenzen122

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A study was made of 200 students to determine what TV shows they watch.
- 22 students hated all Star Trek shows.
- 73 students watch only The Next Generation(TNG).
- 136 students watch TNG.
- 14 students watch only Deep Space 9 (DS9) and Voyager(VOY)
- 31 students watch only TNG and VOY.
- 63 students watch DS9
-135 students do not watch VOY

a) How many students watched all 3?
b) How many watched voyager only?
c) How many students did not watch DS9?

In order for me to solve all three questions. I must construct a venn diagram.
This is what I have so far:
1635786122362.pngAs you can see I put only a few numbers on there and couldn't put the rest simply becauise I was stuck. My next move is to find the number of students who watched all three? How can I find that?
 
EddyBenzen122 said:
A study was made of 200 students to determine what TV shows they watch.
- 22 students hated all Star Trek shows.
- 73 students watch only The Next Generation(TNG).
- 136 students watch TNG.
- 14 students watch only Deep Space 9 (DS9) and Voyager(VOY)
- 31 students watch only TNG and VOY.
- 63 students watch DS9
-135 students do not watch VOY

a) How many students watched all 3?
b) How many watched voyager only?
c) How many students did not watch DS9?

In order for me to solve all three questions. I must construct a venn diagram.
This is what I have so far:
View attachment 29502As you can see I put only a few numbers on there and couldn't put the rest simply becauise I was stuck. My next move is to find the number of students who watched all three? How can I find that?
Click to expand...

You might call that x, and fill in other regions with expressions in x. Eventually, you want to write an equation to solve.
 
lex said:
You have made good progress. You can now use the last two facts in the list, to work out the answer to (a)
Click to expand...
1635805979932.pngI couldn't use the last two facts in the could you show me how?
I tried doing 63 = 14 + x for DS9 I'm so confused at this part
 
Last edited:
You know that there are 135 students outside the VOY circle.
There are 4 sections outside the VOY circle. If you identify them in your diagram, you will see that you know two of them already (in your picture), and don't know the other two. As the total of these 4 sections is 135, you can now work out the total of the those two blank sections.
These two blank sections (which you know the total of), happen to lie within the DS9 circle, which means you now know the total of 3 of the four sections in DS9 (adding on the 14). You know the total of DS9 is 63, which means you now know the final missing section in DS9, which is the answer to (a).
 
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