import math

def binomial_coefficient(n, k):
  return math.factorial(n) // (math.factorial(k) * math.factorial(n - k))

def probability_single_person(n, k):
  p = 0.5 # probability of heads for a fair coin
  probability = 0
  for i in range(k, n + 1):
    probability += binomial_coefficient(n, i) * (p ** i) * ((1 - p) ** (n - i))
  return probability

def probability_at_least_one_person(num_people,
flips_per_person, min_heads):
  single_prob = probability_single_person(flips_per_person,  min_heads)
  return 1 - (1 - single_prob) ** num_people

# Parameters
num_people = 100 # number of people
flips_per_person = 10 # number of coin flips per person
min_heads = 9 # minimum number of heads for success
# Calculate the probability
probability = probability_at_least_one_person(num_people,
flips_per_person, min_heads)

print(f"The probability that at least one person out of {num_people} gets heads at least {min_heads} times is approximately {probability:.4f} or {probability * 100:.2f}%")