Probability of a malicious validator controlling majority of a 6125-size committee

prob.py

import math

def choose(n, k): return math.factorial(n) // math.factorial(k) // math.factorial(n-k)
def prob(n, k, p): return math.exp(math.log(p) * k + math.log(1-p) * (n-k) + math.log(choose(n, k)))
def probge(n, k, p): return sum([prob(n, i, p) for i in range(k, n+1)])

committee = 6125
half = committee / 2

for p in [0.45, 0.46, 0.47, 0.48, 0.49, 0.5, 0.51]:
    print(probge(committee, half, p))

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