Math Prize 2012 Problem 18
Source:
September 24, 2012
probabilityexpected value
Problem Statement
Sherry starts at the number 1. Whenever she's at 1, she moves one step up (to 2). Whenever she's at a number strictly between 1 and 10, she moves one step up or one step down, each with probability . When she reaches 10, she stops. What is the expected number (average number) of steps that Sherry will take?