SHREWD PRISONER'S DILEMMA |
QUESTION |
Because of a prisoner's constant supplication, the king grants
him this favor. He is given 2N balls, which differ from each other
only in that half of them are green and half are red. The king
instructs the prisoner to divide up the balls between two identical
urns. One of the urns will then be selected at random and the
prisoner will be asked to choose a ball at random from the urn
chosen. If the ball turns out to be green, the prisoner will be
freed.
How should he distribute the balls in the urn to maximize his
chances of freedom?
LEARNING OBJECTIVES |
To learn how to formulate a problem probabilistically. After completing
this activity you should be able define compound events of interest,
understand the meaning of conditional probability and law of total
probability.
ACTIVITY |
WARMUP |
Suppose that the prisoner is given 12 balls; 6 green and 6 red.
Let g be the number of green balls and r be the number of red balls in the first urn.
What will be the number of green and red balls in the second urn?
1. What do you think that the best strategy should be?
That is how would you distribute the balls into these urns?