Question

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 9 minutes ago and headed east.”, the owner responded. “He’s probably nine 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:

a. It takes him 1 minute to walk each block (they are short).

b. At the end of each minute interval he is at a corner. There is a 28% chance that he will fall asleep for 1 minute, and an 18% chance that he walk east, or north, or west, or south.

My suggestion is to run at least 1000 trials of the nine-minute journey of the robber.

a. What is the probability he is two blocks or less (walking on streets) from the store?

b. On average how many block has he walked?

c. On average how far away is he (using blocks-no “diagonals”) from the store?

Answer 1

Simulation model is following

Excel Formulas:

C11 =RANDBETWEEN(1,100)

D11 =LOOKUP(C11,$E$2:$E$6,$B$2:$B$6)

E11 =D11

E12 =E11+D12

Copy these formulas down to row 19

Use this model to run 1000 monte carlo simulations.

The results of the model will vary with every simulation run.

On an average he must have wallked 7 blocks (sum of absolute values of Direction - range D11:D19)

On an average he must be 3 blocks away   (absolute value of total distance on 9th minute , cell E19)