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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
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 should approach the ratio of the circle's area to the square's area. Thus, we can write pi/4 = m. Solving for n gives us pi = 4m. 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
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