Description: A student is performing a random walk on the integer number line. Starting at any position > -20 AND < 20, the student flips a coin. If it's heads, the student takes one step to the right or, if tails, one step to the left, and flips again and again until one of the barriers is hit. To Use: Set the Start Position slider to any integer between -20 and +20. Click on the green flag. Note which barrier, the left red one or the yellow one on the right the walker stops at. Intuition tells us that if the walker starts at zero, the probability is 1/2 (0.5) for hitting either barrier. But what if the walker doesn't start at zero? Then one barrier or the other will be closer. What is the probability that the walker, starting at +15, hits the yellow barrier? What is the probability of hitting the red barrier? If you pick a starting position and stick with it for say 100 trials, keeping a record (collecting data) of the number of times each barrier is hit, you will probably be able to form a conjecture as to the P(red) and P(yellow) given the starting point.
In my project Feynman's Random Walk at (http://scratch.mit.edu/projects/11282377/) I coded Dr. Feynman's amazing result that if a random walker starts at zero and performs an n-step random walk, with equal probabilities for moving one step to the right or left, and with no barriers left or right, then the 'average displacement of the walker is √(n). In this project, barriers are placed on opposite sides of zero and the random walker, starting at any point between the barriers, random walks until a barrier is hit. Given that the walker starts at a position between the barriers, what is P(red) and P(yellow) if the red barrier is at -20 and the yellow barrier is at +20? Dr. Arthur Wiebe solved the problem theoretically and provided two proofs. I have copies of each proof.
