Have you really lost your marbles?

Logic Level 2

I have four boxes, each containing a number of red marbles and blue marbles.

Box ABox BBox CBox D
Red marbles \text{Red marbles}7070yy2277
Blue marbles\text{Blue marbles}30303398985353

If the probability of randomly selecting a red marble from Box A is aa, and the probability of randomly selecting a red marble from Box B is bb, then a<ba < b.

Suppose we group all the marbles in Box A and Box C into another Box AC; likewise we group all the the marbles in Box B and Box D into another Box BD. Now, there is a higher probability of randomly selecting a red marble from Box AC than from Box BD.

What is the sum of the smallest and the largest possible values of yy for which the above criteria is satisfied?

Image Credit: Flickr Lyle.
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