Suppose you are out on the town with friends and you all end up at a local casino. The rules at one table are as follows: You win $1 if the die comes up with an odd number and you lose $1 if it comes up even.
A) Suppose you get 22 odd numbers in your first 50 rolls. How much have you won or lost?
B) On the second 50 rolls, your luck improves and you roll 24 odd numbers. How much have you won or lost over 100 rolls?
C) You luck continues to improve, and you roll 74 odd numbers in you next 150 rolls. How much have you won or lost over your total of 250 rolls?
D) How many odd numbers would you have to roll in the next 50 rolls to break even? Is this likely? Explain.
E) What were the percentages of odd numbers after 50, 100, and 250 rolls? Explain how this illustrates the law of large numbers, even while your losses increased.