Suppose there are four boxes, labeled A1 , A2 , B1 , B2 . Each of the boxes cont

Question

Suppose there are four boxes, labeled A1, A2, B1, B2. Each of the boxes contains a mixture of red and blue balls. Give an example of how the balls could be distributed so that following are all true:

(a) A1 has a higher percentage of red balls than B1.

(b) A2 has a higher percentage of red balls than B2.

(c) If we merge the contents of A1 and A2 into a new box A1,2, and merge the contents of B1 and B2 into another new box B1,2, then A1,2 has a lower percentage of red balls than B1,2.

(Your answer should consist of numbers of red balls in each of the original boxes, along with a calculation showing that the conditions are satisfied.)

Explanation / Answer

Let A1 have 2 Red and 19 Blue ball (9.52% Red)

Let B1 have 1 Red and 10 Blue balls (9.1%Red)

So, A1 is having more perecentage of red balls than B1

Let A2 have 10 Red and 9 Blue balls (52.6% Red)

Let B2 have 9 Red and 9 Blue balls (50% Red)

Here, A2 is having more percentage of red balls

After mixing A1,2 will have 12 Red and 28 Blue balls (30% Red)

B1,2 will have 10 Red and 19 Blue ball (34% Red)

So, A1,2 is having lower percentage of Red balls than B1,2

All conitions are satisfied in the above distribution

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