import random

def random_kid():
    return random.choice(["boy", "girl"])

both_girls = 0
older_girl = 0
either_girl = 0

random.seed(0)

N=100000

for _ in range(N):

    # Do experiment
    younger = random_kid()
    older = random_kid()

    # Tally successes
    if older == "girl":
        older_girl += 1

    if older == "girl" and younger == "girl":
        both_girls += 1

    if older == "girl" or younger == "girl":
        either_girl += 1

# P(A | B) = P(A,B) / P(B)

# probability of the event “both children are girls” (A) 
# conditional on the event “the older child is a girl” (B)
#  = P(both) / P(older_girl)

print("P(both | older):", both_girls / older_girl) 	# 0.514 ~ 1/2

# probability of the event “both children are girls” (A) 
# conditional on the event “at least one of the children is a girl” (B)
#  = P(both) / P(either_girl)

print("P(both | either): ", both_girls / either_girl) 	# 0.342 ~ 1/3