Lecture Notes on 14 July 2014

# Solution to Samuel Pepys problem
import random

def main():
  # number of trials
  num_trials = 1000

  # trial 1: 6 throws of a fair die
  trial_1 = 0
  for i in range (num_trials):
    is_six = 0
    for j in range (6):
      if (random.randint (1, 6) == 6):
        is_six += 1
    if (is_six >= 1):
      trial_1 += 1
  print ('Trial 1: ', trial_1, '/', num_trials)

  # trial 2: 12 throws of a fair die
  trial_2 = 0
  for i in range (num_trials):
    is_six = 0
    for j in range (12):
      if (random.randint (1, 6) == 6):
        is_six += 1
    if (is_six >= 2):
      trial_2 += 1
  print ('Trial 2: ', trial_2, '/', num_trials)

  # trial 3: 18 throws of a fair die
  trial_3 = 0
  for i in range (num_trials):
    is_six = 0
    for j in range (18):
      if (random.randint (1, 6) == 6):
        is_six += 1
    if (is_six >= 3):
      trial_3 += 1
  print ('Trial 3: ', trial_3, '/', num_trials)

main()

# Solution to the Birthday Paradox Problem
import random

def compute_prob (num_students, num_trials):
  same_bday = 0
  for i in range (num_trials):
    bdays = ''
    is_same = 0
    for j in range (num_students):
      # generate random birthdays and check
      b_num = random.randint (1, 365)
      b_str = ":" + str (b_num) + ":"
      if (bdays.find (b_str) > -1):
        is_same += 1
      bdays = bdays + b_str
    if (is_same > 0):
      same_bday += 1
  print ('Students ' + str (num_students) + ' : ' + str (same_bday) + \
  ' / ' + str (num_trials))

def main():
  num_trials = 1000

  for i in range (2, 366):
    compute_prob (i, num_trials)

main()