Have you really lost your marbles?

Logic Level 3

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

Box ABox BBox CBox 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?

Image Credit: Flickr Lyle.
×

Problem Loading...

Note Loading...

Set Loading...