KEY
PROBABILITY PROJECT A
Warren Hills Middle School has decided to run the following
spinner game as a fundraiser at a local carnival.
MAKING PURPLE
Spin each spinner once. Blue and
red make purple so if one lands
on red and the other lands on
blue, YOU WIN!!!
Task One: Research “theoretical probability” and
“experimental probability”. Explain each using an example.
Theoretical Probability is the likelihood an event SHOULD happen.
It is obtained by analyzing the situation. You can use a tree
diagram to determine it.
Example: If you roll a dice, the theoretical probability of getting a 2
is 1/6 because you have 6 equally likely outcomes and only one
will give you the 2.
Experimental Probability is ratio (fraction) of the times an event
ACTUALLY occurred to the times it was attempted. It’s found by
experimenting & recording your results.
Example: I flipped a coin 20 times and got heads 11 times. The
experimental probability of getting heads is 11/20.
Task Two: What is the experimental probability of winning
this game if you play this game 45 times? Explain
mathematically how you determined this.
Answers Vary – For example, if 4/45 was my experimental probability…
I played the game 45 times and kept track of my wins and losses. I only
won 4 out of the 45 times I played.
Task Three: Draw a tree diagram of the two spins to play
this game.
Red
R B G
Green
R B G
Red
R B G
Blue
R B G
Red
Yellow
R B G
R B G
RR RB RG GR GB GG RR RB RG BR BB BG RR RB RG YR YB YG
Task Four: What is the theoretical probability of winning
this game if you play it 45 times? Explain mathematically
how you determined this.
The theoretical probability of winning is 4/18 = 2/9. I determined this by
listing all possible outcomes below my tree diagrams. Since they are each
equally likely and there are four ways to get Red and Blue in one turn, the
probability is 4 out of 18 = 4/18 = 2/9.
KEY
PROBABILITY PROJECT B
The rescue squad and the fire department decide to run following
probability games as fundraisers at the town carnival.
Support the Rescue
Squad!
Cost to Play: $1.50
Winners get $5
Spin this spinner once.
If you spin a red,
YOU WIN!!
Help the Fire
Fighters!
Cost to Play: $2
Winners get: $5
Roll a die. If you roll a
number greater than 4,
YOU WIN!!
Task One: Explain the theoretical probability of winning each game.
¼ chance to win because if the
2/6 = 1/3 chance to win because the
spinner were in equal sections there only numbers greater than 4 are the
would be 1 red section out of 4 total 5 & 6. Two possible rolls will let you
sections.
win out of six possible rolls you
could get.
Task Two: As a player, explain which game would be to your best
advantage to play and why?
I would be better off playing the FireFighter’s Dice game because 1/3 of the
chance is a better chance to win than ¼ is.
Task Three: If 48 people play each, find the following for each game:
How much money will they take in?
How many people should they expect to win?
How much money should they expect to pay out to winners?
How much profit should they make?
48 people x $1.50 = $72.00 taken in
48 people x $2 = $96.00 taken in
¼ of 48 = 12 expected winners
12 winners x $5 = $60 to winners
$72 in - $60 out = $12 profit
1/3 of 48 = 16 expected winners
16 winners x $5 = $80
$96 in - $80 out = $16 profit
Task Four: The rescue squad and fire fighters decide to work together and
run only one of these game booths at the carnival. Which of these should
they choose? Explain your choice mathematically.
They should run the FireFighter’s Dice Game because the expected profit is
higher. You can see this because for every 48 people that play you make $4
more profit for that game than for the Rescue Squad game.