Lecture Notes on 13 Oct 2017

Pepys Problem: Which is more probable at least one six in six throws
of a fair die or at least two sixes in twelve throws of a fair die.

import random

def is_successful (num_throws, sixes):
  num_six = 0
  throw = 0
  while (throw < num_throws):
    if (random.randint(1,6) == 6):
      num_six += 1
    throw += 1
  return (num_six >= sixes)

def main ():
  # input number of trials from the user
  num_trials = int (input ('Enter number of trials: '))

  # scenario 1: 6 throws of a die
  trial = 0
  num_success = 0
  while (trial < num_trials):
    if (is_successful (6, 1)):
      num_success += 1
    trial += 1
  print ('Scenario 1: ', num_success, '/', num_trials)

  # scenario 2: 12 throws of a die
  trial = 0
  num_success = 0
  while (trial < num_trials):
    if (is_successful (12, 2)):
      num_success += 1
    trial += 1
  print ('Scenario 2: ', num_success, '/', num_trials)

main()