Question

This problem deals with continuous (rather than discrete) probability, but it's an interesting problem! It involves probabilistically estimating the value of pi. Consider a circle of radius 1 inscribed within a square with side 2. Both shapes are centered at the origin (0, 0). Using basic geometry, the ratio of the circle's area to the square's area is pi (1)^2/2^2 = pi/4. Now, suppose that you randomly throw some darts at this figure. Out of n total attempts, m attempts land within the circle. As the number of attempts becomes large, the ratio m/n should approach the ratio of the circle's area to the square's area. Thus, we can write pi/4 = m/n. Solving for pi gives us pi = 4m/n. Write a Python program that allows the user to enter a value for n (the total number of attempts). Your program should then simulate throwing n darts at the figure by randomly picking coordinates (x, y) between -1.0 and 1.0. Keep track of the darts that land within the circle, and show the resulting estimate for pi. Python Python's random() function (located in the random module) behaves the same as Java's Math.random() - it returns a uniformly distributed pseudorandom real number in the interval [0.0, 1.0). To call it: import random x = random. random()

Answer 1

from random import uniform
from math import sqrt

def getRandomPoint():
return uniform(-1, 1)

def isInUnitCircle(x, y):
if sqrt(x*x + y*y) <= 1:
return True
else:
return False

n = int(input("Enter n: "))
count = 0
for i in range(0, n):
x = getRandomPoint()
y = getRandomPoint()
if isInUnitCircle(x, y):
count += 1

pie = (4.0*count)/n

print("Calculated value of pi = %f" % (pie))

# pastebin link: https://pastebin.com/X9YQsTJi