# Have you really lost your marbles?

**Logic**Level 3

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?