Lesson 2

Of course, \(001\), like any other combination of three bits, appears with a probability of \(\frac{1}{8}=0.125\). It is unclear how one of these combinations could be more likely than another. Below, we will see examples where (again counterintuitively) some combinations turn out to be better than others.

Problem. We will keep flipping the coin until the last three flips result in either \(000\) or \(111\). What is the probability that \(000\) appears before \(111\)?