A robbery has just been committed at the Corner Market in the downtown area of the city. The market owner was able to activate the alarm, and the robber fled on foot. Police officers arrived a few minutes later and asked the owner, “How long ago did the robber leave?” “He left about 10 minutes ago and headed east.”, the owner responded. “He’s probably ten blocks away by now.”, one of the officers said to the other. “Not likely”, said the storeowner. “He was so stoned on drugs that I bet he’s still only within a few blocks of here! He’s probably just running in circles!”
Perform a simulation experiment that will test the storeowner’s hypothesis.
Assume the following:
• It takes him 1 minute to walk each block (they are short).
• At the end of each minute interval he is at a corner. There is a 20% chance that he will fall asleep for 1 minute, or walk east, or walk north, or walk west, or walk south. Run at least 1000 trials of the ten-minute journey of the robber.
a. What is the probability he is two blocks or less (walking on streets) from the store?
b. What is his average walking distance (using blocks-no “diagonals”) from the store?