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.

• Suppose you get 22 odd numbers in your first 50 rolls.  How much have you won or lost?

• On the second 50 rolls, your luck improves and you roll 24 odd numbers.  How much have you won or lost over 100 rolls?

• 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?

• How many odd numbers would you have to roll in the next 50 rolls to break even?  Is this likely? Explain.

• 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.

Part 1

50 - 22 = 28

22 * 1 + 28 * (-1) = 22 - 28 = -6 dollars

odd                    even                       total #

22                        28                             50

You lost 6 dollars.

part 2

50 - 24 = 26

24 * 1 + 26 * (-1) = 24 - 26 = -2 dollars

odd             even                  total #

22                28                       50

24                26                       50

------------------------------------------

sub-

total     46                54                       100

You lost 8 dollars.

answered May 18, 2012 by Level 10 User (55,660 points)

part 3

150 - 74 = 76

74 * 1 + 76 * (-1) = 74 - 76 = -2 dollars

odd even total #

22 28 50

24 26 50

74 76 150

-----------------------------------------------------

sub-

total 120 140 250

You lost 20 dollars.

part 4

To break even means that the answer is equal to 0, or you have an equal

number of odd and even rolls.

odd even total #

22 28 50

24 26 50

74 76 150

30 20 50

-----------------------------------------------------

sub-

total 150 150 300

therefore to break even and toatl 150 in both of the odd and even columns, you need 30 odd rolls, and 20 even rolls.

answered May 18, 2012 by Level 10 User (55,660 points)

part 5

The percentage at 50 rolls is 22/50 = 44%

The percentage at 100 rolls is 46/100 = 46%

The percentage at 250 rolls is 120/250 = 48%

From observation It looks as if you increase 2% with every 50 rolls. So to break even you need 50 more rolls. To win you need another 50 rolls.

answered May 18, 2012 by Level 10 User (55,660 points)