You have been captured by an evil wizard. However the wizard also likes maths, and sets you a challenge. You have two identical vases, and 100 white beads and 100 black beads. You must arrange the beads however you like between the two vases. The only condition is that no vase can be empty. And all the beads must be in the vases.The wizard will then get his assistant to choose a single bead from one of the vases. The assistant will pick purely at random, and will not peek! If the assistant picks a black bead, you will go free. If the assistant picks a white bead... well, let's not go there. Obviously you would like the assistant to pick a black bead. The question is this. How do you arrange the beads so as to give yourself the best chance of freedom?

There are no tricks. Just mathematics.

The answer is given on the next page.

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.