[math-fun] Cute probability problem
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? --Dan ________________________________________________________________________________________ It goes without saying that .
From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Sent: Sunday, March 4, 2012 10:13 AM Subject: [math-fun] Cute probability problem
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?
--Dan
----------------------------------------------------------------------- f(p) = (2p - 1)/p^2 for p > 1/2, f(p) = 0 for p <= 1/2. -- Gene
participants (2)
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Dan Asimov -
Eugene Salamin