The equalization probability of the Pólya urn
TC Wallstrom - The American Mathematical Monthly, 2012 - Taylor & Francis
TC Wallstrom
The American Mathematical Monthly, 2012•Taylor & FrancisWe consider a Pólya urn, started with b black and w white balls, where b> w. We compute
the probability that there are ever the same number of black and white balls in the urn, and
show that it is twice the probability of getting no more than w− 1 heads in b+ w− 1 tosses of a
fair coin.
the probability that there are ever the same number of black and white balls in the urn, and
show that it is twice the probability of getting no more than w− 1 heads in b+ w− 1 tosses of a
fair coin.
Abstract
We consider a Pólya urn, started with b black and w white balls, where b > w. We compute the probability that there are ever the same number of black and white balls in the urn, and show that it is twice the probability of getting no more than w − 1 heads in b + w − 1 tosses of a fair coin.
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