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March 4th, 2012, 04:35 AM   #1
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Set theory help.

I believe I got this question correct but would like someone else to check.

There is a total of 200 school children who eat certain types of sweets.

- 130 pick the red one. = (R)
- 90 take the blue one. = (B)
- 84 take the purple one. = (P)

Out of these

- 40 Take R & B
- 50 Take R & P
- 30 Take B & P

Find students who take all three sweets?
Red Only = 130 - 40 - 50 = 40
Blue Only = 90 - 30 - 40 = 20
Purple Only = 84 - 30 - 50 = 4
Then we have the students who take both.
40 Take R & B
50 Take R & P
30 Take B & P

So

40+20+4+40+50+30 = 184

200 - 184 = 16

16 Student take all three sweets.


Red and blue but not purple?
We already know 40 take R & B

Only Blue sweets ?
90 - 40 - 30 = 20

Could someone check the maths is correct here thanks.
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March 4th, 2012, 05:32 AM   #2
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Re: Set theory help.

If A, B and C are any three events,


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March 4th, 2012, 06:01 AM   #3
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The original calculations are incorrect. I'll assume that each child takes at least one of the types mentioned.
Note that the count of those who take R and B includes those who take all three types.

The number who take R or B is 130 + 90 - 40 = 180. Hence 20 take only P.
The number who take R or P is 130 + 84 - 50 = 164. Hence 36 take only B.
The number who take B or P is 90 + 84 - 30 = 144. Hence 56 take only R.

Of the 130 who take R, 74 take B or P, of which 40 take B and 34 take only R and P.
Of the 90 who take B, 54 take P or R, of which 30 take P and 24 take only B and R.
Of the 84 who take P, 64 take R or B, of which 50 take R and 14 take only P and B.

Of the 50 who take R and P, 34 take only R and P, so 16 take R, B and P.
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March 4th, 2012, 09:16 AM   #4
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Re:

Quote:
Originally Posted by skipjack

Of the 130 who take R, 74 take B or P, of which 40 take B and 34 take only R and P.
Where do you get the 74 from?
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March 4th, 2012, 09:34 AM   #5
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Re: Set theory help.

Don't worry, I understand now. Thanks for the explanation.
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