Re: [math-fun] Cute probability problem

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