Here you will find some scripts that I used to solve the first set of challenge questions. I recommend viewing them with IPython Notebook, or alternateively, you can simply view the code and execute in an IPython environment.
In order to solve for the random walk questions, I imagined what I knew about other random walk scenarios. I recalled a story from the scientists at Los Alamos National Laboratory, and decided a Monte Carlo simulation was a workable idea.
####1. createTheData.ipynb
This script generates a JSON file which contains the random walks. I found that random.randint() was significantly less random than random.choice('True','False').
####2. siftAndPlot.ipynb
I wrote this code to assess my 'random' data and to make sure it simulated what I wanted it to simulate.
####3. calculations.ipynb
This IPython Notebook contains the expressions that I used to find my actual responses.
NOTE: Due to the limitations of my laptop, I ran this simulation for 500k trials. However, this test can be done with many more data points.