import random

# Problem:
# 2.11
# At a completely random moment between 6:30 and 7:30 a.m.,
# the morning newspaper is delivered to Mr. Johnson’s residence.
# Mr. Johnson leaves for work at a completely random moment
# between 7:00 and 8:00 a.m. regardless of whether the newspaper 
# has been delivered. What is the probability that Mr. Johnson can 
# take the newspaper with him to work? Use computer simulation to 
# find the probability.
#
# Solution:
#      Applying Bayes' theorem.
#      Newsletter arrives in interval 6:30 - 7:00 ?
#          yes| p=0.5                    no| p=0.5
#             |              Mr. Jonhnson leaves in interval 7:00 - 7:30
#             |                      yes| p=0.5             no| p=0.5
#             |             Newsletter arrives first in       |
#             |                 interval 7:00-7:30            |
#             |                yes| p=0.5       no| p=0.5     |
#             |                   |                           |
#            0.5     +       0.5*0.5*0.5      +            0.5*0.5 = 0.875
#
# Simulation:
#       0.874867
#       0.874876
#       0.874876
#

newspaper_arrived_on_time = 0
samples = 10000000
for i in range(samples):
    n = random.random()
    w = random.random() + 0.5
    if w >= n:
        newspaper_arrived_on_time += 1

print('simulated probability of ontime arrived newspaper is : {}'
      .format(newspaper_arrived_on_time/samples))