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GRE 2-A box contains either blue or red flags...

By spartan
A box contains either blue or red flags. The total number of flags in the box is an even number. A group of children are asked to pick up two flags each. If all the flags are used up in the process such that 60% of the children have blue flags, and 55% have red flags, what percentage of children have flags of both the colors? A) 5%
B) 10%
C) 15%
D) 20%
E) It can not be determined

 In this problem, let A be the event that a child picks up a blue flag, B be the event that a child picks up a red flag. Then, A∪B is the event that the child picks up either a blue or a red flag, and A∩B is the event that the child picks up both a blue and a red flag.
  1. From the problem statement we know:
    I. P(AUB) = 100% (Since there are even number of flags and all the flags in the box are taken by the children)
    II. P(A) = 60%
    III.P(B) = 55%
    IV. P(A∩B)=?
  2. We are trying to find the percentage of children who have flags of both the colors. Substituting the values from (3.) into the equation given in (1.) we get:
  3. P(A∪B) = P(A) + P(B) - P(A∩B)
    100% = 60% + 55% - P(A∩B)
    P(A∩B) = (60% +55%)-100%
    P(A∩B) =115%-100%
    P(A∩B) =15%
    Therefore the percentage of children who got both a red flag and a blue flag is 15%. Thus, C is the correct answer choice.
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