The game requires $5 to play, once the player is admitted, he
or she has the opportunity to take a chance with luck and pick from
the bag. If the player receives a M&M, the player loses. If the
player wins a Reese’s Pieces candy, the player wins. If the player
wins they may roll a dice for a second turn, if the die rolls on a
even number, they may pick from the bag once again with no extra
charge, if the player rolls a odd, their turn is over.
The outcome of this game can be shown as the following: Paying
the $5 for entry fee gets the player into the game where they face
a 4/79 chance of winning and a 75/79 chance of losing for the first
phase. This phase is shown as the following:
300 M&M’s + 16 Reese’s Pieces=316 Total Counts
Winning: 16/316 which is 4/79 chance ( M&Ms are possible
choices out of total count)
Losing: 300/316 which is 75/79 chance (Reece’s Pieces are
possible choices out of total count)
If the player happens to win, they have a second chance to
continue by rolling a single die. If they player can land the die
on a even number, they may turn the knob of the machine once again,
if they land on a odd number the player ends their turn completely.
This following by rolling the die gives the player a ½ win or lose
chance. There are the same number of even and odd numbers on a 6
1 2 3 4 5 6
Even numbers: 3/6 which is ½ chance of winning ( 2,4,6 )
Odd numbers: 3/6 which is ½ chance of losing ( 1,3,5 )
* Is the game fair? Show the mathematical calculations for the
expected value of winning the game.
* If the game is not fair, how could you change the game to
make it fair?
* What are the probabilities for each outcome?