Challenge: Solving the Task Using Geometric Probability
Consider a square with a side length of 2 units centered at the origin (0, 0) in a Cartesian coordinate system.
What is the probability that a randomly chosen point within the square doesn't fall into a circle with a radius of 1 unit centered at the origin?
As we have a two-dimensional space of elementary events, we can calculate the ratio of the circle's area to the square's area. The ratio represents the probability of a point falling within the circle.
Tarea
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Calculate probability as the ratio between the blue area and the whole area of the square.
Solución
import numpy as np
import matplotlib.pyplot as plt
# Define the radius of the circle and the side length of the square
radius = 1
side_length = 2
# Calculate the area of the circle and the square
circle_area = np.pi * radius**2
square_area = side_length**2
# Calculate the probability that point doesn't fall into a circle
probability = (square_area - circle_area) / square_area
# Print the solution
print(f'The probability that a randomly chosen point within the square do not fall into a circle is {probability:.4f}')
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Sección 1. Capítulo 4
import numpy as np
import matplotlib.pyplot as plt
# Define the radius of the circle and the side length of the square
radius = 1
side_length = 2
# Calculate the area of the circle and the square
circle_area = np.pi * radius**2
square_area = side_length**2
# Calculate the probability that point doesn't fall into a circle
probability = (___ - ___) / square_area
# Print the solution
print(f'The probability that a randomly chosen point within the square do not fall into a circle is {probability:.4f}')
