Pólya's Urn
An urn starts with one red and one blue ball. Repeatedly, a ball is drawn uniformly at random, then returned along with one additional ball of the same color. What is the probability the third draw is red? Express as a fraction.
Related problems & prerequisites
Worth solving first
- All in a Semicircle 6.0/10
- The Sock Drawer 5.0/10
Source: The Polya urn, introduced by Florian Eggenberger and George Polya (1923). Statement written for AxiomIQ.