Birthday paradox / problem. In a room of 70 people, there's a 99.9% chance that there will be a pair with the exact same day of birth.

birthday.py

# In probability theory, the birthday paradox concerns the probability that,
# in a set of n randomly chosen people,
# some pair of them will have the same birthday.
# By the pigeonhole principle, the probability reaches 100% when
# the number of people reaches 367.

import random

# 365 distinct birthdays including February 29th.
birthdays = 365

# Returns true if two people out of n_people have the same birthday.
def birthday(n_people):
	distinct_dates = set()
	for person in range(n_people):
		birthdate = random.randrange(birthdays + 1)
		if birthdate in distinct_dates:
			return True
		else:
			distinct_dates.add(birthdate)
	return False


def simulations(n_people, trials):
	successes = 0
	for trial in range(trials):
		if birthday(n_people):
			successes += 1
	return successes/trials

if __name__ == '__main__':
	print(simulations(23, 10000)) # 50% chance with only 23 people.
	print(simulations(70, 10000)) # 99.9% chance with 70 people.
	print(simulations(366, 10000)) # 100% because pigeonholed.