SIMULATION MODELING AND ANALYSIS $|$

Write a Python Code for following: A prisoner is trapped in a cell containing five doors. The

first door leads to a tunnel which returns to his cell after three days of travel. The second leads to a

tunnel which returns him to his cell after a single day of travel. The third door leads him

immediately to freedom. The fourth door leads to a tunnel that will take him to freedom after two

days of travel. Assuming that the prisoner will always select doors $1,2,3$ and $4$ with probabilities

$0\mathrm{.}38,0\mathrm{.}21,0\mathrm{.}23,$ and $0\mathrm{.}18$ respectively, simulate the system for $n=20,50,100,500,1000$ times to

compute the expected number and variance of days until the prisoner reaches freedom.

Note: Please, do not use any Markov Chain related probability calculations you learnt in EMU$321$

course.