4 Mar
2012
4 Mar
'12
10:01 p.m.
From: Dan Asimov <dasimov@earthlink.net> I saw this problem in some stuff I was reading: Consider the standard binary tree with infinitely many levels. Suppose each edge is colored green with probability = p. What is the probability f(p) that there exists an infinite green path starting at the root?
--Let q=1-p and g(p)=1-f(p). Then g(p) obeys g(p) = q^2 + p*q*2*g(p) + p^2 * g(p)^2 you may now solve the quadratic equation to deduce g(p) and hence f(p). Don't choose the wrong root.