# Have you really lost your marbles?

Logic Level 3

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

 Box A Box B Box C Box D $\text{Red marbles}$ $70$ $y$ $2$ $7$ $\text{Blue marbles}$ $30$ $3$ $98$ $53$

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

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 $$y$$ for which the above criteria is satisfied?

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