import numpy as np import random Total_Iterations = 10000 n = 1000 k = 240 p = 0.25 q = 1- 0.25 hits = 0 for iteration in range(Total_Iterations): sample = np.random.random((n,)) count = np.count_nonzero(sample < 0.25) if count >= k: hits+=1 result = hits/Total_Iterations print("Using simulation: ",result)

from scipy import special n = 1000 k = 240 p = 0.25 q = 1-0.25 result = 0 for i in range(k, n+1): result += special.comb(n,i) * (p**i) * ((1-p)**(n-i)) print("Using Binomial Distribution: ", result)