Please help.. this is a 5 part answer... PLEASE HELP

Question

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.

Answer 1

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.

 

Answer 2

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.

 

Answer 3

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.