write code below with import random function do not use numpy #New Updated Code

import numpy as np

import matplotlib.pyplot as plt

import math

import time

# Calculate pi using Monte Carlo method

def cal$\_$pi$($num$\_$points$)$:

x $=$ np$.$random.uniform$(-1,1,$ num$\_$points$)$

y $=$ np$.$random.uniform$(-1,1,$ num$\_$points$)$

in$\_$circle $=$ x$**2+$ y$**2<=1$

pi$\_$est $=4*$ np$.$sum$($in$\_$circle$)/$ num$\_$points

return pi$\_$est

# Function to calculate percent error

def per$\_$error$($est$\_$pi$)$:

return math.fabs$(($est$\_$pi $-$ math.pi$)/$ math.pi$)*100$

# Number of points to test

points $=[10,100,1000,10000,100000,1000000]$

errors $=[]$

# Calculate percent error for each number of points

for num$\_$points in points:

pi$\_$est $=$ cal$\_$pi$($num$\_$points$)$

error $=$ per$\_$error$($pi$\_$est$)$

errors.append$($error$)$

print$($f$"$Points: $\{$num$\_$points$\},$ Pi Estimate: $\{$pi$\_$est$\},$ Percent Error: $\{$error:$\mathrm{.}2$f$\}\%")$

# Plotting the percent error

plt$.$figure$($figsize$=(10,6))$

plt$.$plot$($points$,$ errors, marker$=\text{'}$o$\text{'},$color$=$'green', linestyle$=$'dashed'$)$

plt$.$xscale$(\text{'}$log$\text{'})$

plt$.$xlabel$(\text{'}$Points$\text{'})$

plt$.$ylabel$(\text{'}$Percent Error'$)$

plt$.$title$(\text{'}$Monte Carlo Method Percent Error in Pi Calculation via Numpy'$)$

plt$.$grid$($True$)$

plt$.$show$()$

n$\_$samples $=100$

start $=$ time.time$()$

end $=$ time.time$()$

elap$\_$time$\_100=$ end $-$ start

print$($f$"$Elapsed time for $\{$n$\_$samples$\}$ samples: $\{$elap$\_$time$\_100\}$ seconds"$)$

n$\_$samples $=10000000$

start $=$ time.time$()$

end $=$ time.time$()$

elap$\_$time$\_10000000=$ end $-$ start

print$($f$"$Elapsed time for $\{$n$\_$samples$\}$ samples: $\{$elap$\_$time$\_10000000\}$ seconds"$)$

# Measure performance for $1,000$ steps

n$\_$steps $=1000$

start $=$ time.time$()$

end $=$ time.time$()$

elap$\_$time$\_1000\_$steps $=$ end $-$ start

print$($f$"$Elapsed time for $\{$n$\_$steps$\}$ steps: $\{$elap$\_$time$\_1000\_$steps$\}$ seconds"$)$