ORIGINAL CODE:

# In this simulation the library numpy is used and it is named it $"$np$"$

import numpy as np

# The seed below initializes the random generator to always obtain the same result.

# DO NOT CHANGE THIS VALUE AND RERUN THIS CELL EVERYTIME YOU RUN THE PROGRAM.

np$.$random.seed$(3500)$

# Variables are defined in this cell

v $=16/60$ # Rate of vehicles per second

queueMoveTime $=1\mathrm{.}5$ # Time it takes a vehicle to clear the intersection

redTime $=60$ # Red light time in seconds

greenTime $=60$ # Green light time in seconds

nVehi $=0$ # Number of vehicles arriving at the intersection

nRep $=0$ # Counter for number of repetitions

nQueue $=0$ # Counter for number of times vehicles queue

isRed $=$ True # Initialize the light as red

isGreen $=$ False

# Monte Carlo simulation

nsim $=100000$ # Number of simulation

while nRep $$ nsim:

# Red light cycle

if isRed:

nRep $=$ nRep $+1$ # Count replicates

nVehi $=$ nVehi $+$ np$.$random.poisson$($v $*$ redTime$)$

isRed $=$ False

isGreen $=$ True

# Green light cycle

else:

time $=$ queueMoveTime

while isGreen:

if nVehi $>0$:

nVehi $=$ nVehi $-1$

nVehi $=$ nVehi $+$ np$.$random.poisson$($v $*$ queueMoveTime$)$

else:

break

time $=$ time $+$ queueMoveTime

if time $>=$ greenTime:

break

if nVehi $>0$:

nQueue $=$ nQueue $+1$

# Reset light to Red

isRed $=$ True

isGreen $=$ False

# Calculate the probability of queuing

pQueue $=$ nQueue $/$ nsim

print$("$The probability of queuing at the intersection is $",$ pQueue$).$ Answer question in image using this info.