Well, it’s our old friend the mysterious pouch. Today the pouch contains a random quantity of marbles, and we’re going to withdraw a handful. But first, consider:

• If the bag contains an even number of marbles, then we are equally likely to withdraw an even or an odd number. For instance, if it contains 4 marbles, then we are equally likely to withdraw 2 or 4 as 1 or 3.
• But if the pouch contains an odd number of marbles, then we’re more likely to withdraw an odd number, as there’s one more way of choosing an odd number than an even number. For example, if the pouch contains 5 marbles then we’re more likely to draw 1, 3, or 5 than 2 or 4.

This is troubling. Without even opening the pouch we seem to have decided that, on balance, we’re more likely to withdraw an odd number of marbles than an even. Indeed, this seems to mean that handfuls in general are more commonly odd than even. How can this be?