Bead Puzzle - Page 2
Place a single black bead in one vase. Place all the other beads in the other vase.
There is a 50% chance that the wizard's assistant will pick the vase with the single black bead in it, in which case you will go free.
However there is a 50% chance that the assistant will pick the other vase, in which case there is a 49.75% chance of picking a black bead.
Overall, the chance of the assistant picking a black bead and you going free is 74.87%. Not perfect, but a lot better than 1 in 2 or 50%, which it would have been if the beads had all been mixed together in a single vase.