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 March 4th, 2012, 04:35 AM #1 Member   Joined: Feb 2012 Posts: 31 Thanks: 0 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.
 March 4th, 2012, 05:32 AM #2 Senior Member   Joined: Jan 2012 Posts: 131 Thanks: 0 Re: Set theory help. If A, B and C are any three events, $P(A \cup B \cup C)=P(A) +P(B) + P(C) -P(A \cap B) -P(B \cap C) - P(C \cap A) + P(A \cap B \cap C)$ $200=130 + 90 + 84 -40 -30-50 +P(A \cap B \cap C)$ $P(A \cap B \cap C)=16$
 March 4th, 2012, 06:01 AM #3 Global Moderator   Joined: Dec 2006 Posts: 20,969 Thanks: 2219 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.
March 4th, 2012, 09:16 AM   #4
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 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?

 March 4th, 2012, 09:34 AM #5 Member   Joined: Feb 2012 Posts: 31 Thanks: 0 Re: Set theory help. Don't worry, I understand now. Thanks for the explanation.

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