maximizing probability in balls and urns
Source: French MO 2000 Exercise 1
April 9, 2021
probabilitycombinatorics
Problem Statement
We are given white balls and black balls () which are to be distributed among two urns, at least one in each. Let be the number of balls in the first urn, and the number of white ones among them. One randomly chooses an urn and randomly picks a ball from it.(a) Compute the probability that the drawn ball is white.
(b) If is fixed, for which is maximal?
(c) Find the distribution of balls among the urns which maximizes .
(d) Give a generalization for larger numbers of colors and urns.