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 only a few minutes ago,” the store owner responded. “He’s probably 10 blocks away by now,” one of the officers said to the other. “Not likely,” said the store owner. “He was so stoned on drugs that I bet even if he has run 10 blocks, 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 store owner’s hypothesis. Assume that at each corner of a city block there is an equal chance that the robber will go in any one of the four possible directions: north, south, east, or west. Simulate for five trials and then indicate in how many of the trials the robber is within 2 blocks of the store.