Let X1, . . . , Xn be independent random

Let X₁, . . . , X_n be independent random variables each uniformly distributed on [−1, 1]. Let p_n = P(X²₁ + · ·   + X²_n < 1). Conduct a simulation study to approximate p_n for increasing values of n. For n = 2, p₂ is the probability that a point uniformly distributed on the square [−1, 1] × [−1, 1] falls in the inscribed circle of radius 1 centered at the origin. For n = 3, p₃ is the probability that a point uniformly distributed on the cube [−1, 1] × [−1, 1] × [−1, 1] falls in the inscribed sphere of radius 1 centered at the origin. For n > 3, you are in higher dimensions estimating the probability that a point in a “hypercube” falls within the inscribed “hypersphere.” What happens when n gets large?