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Creating Tree Diagrams to find Theoretical Probability
We are learning to…find the theoretical probability of an event.
Tuesday, April 18, 2023
Vocabulary
Theoretical Probability - Probability that is based on likelihood of an event happening based on all the possible outcomes. One way to determine theoretical probability
is to build a TREE DIAGRAM A Tree Diagram is a way to visually
represent and organize all the possible outcomes of an experiment.
Ice Cream:Chocolate
VanillaStrawberry
Mint
Toppings:Sprinkles PeanutsBananas
Sauce:Hot FudgeCaramel
Warren owns an Ice Cream Shop and had the sign below made to let people know what they can order:
Make a tree diagram to find all of the possible outcomes of ice cream, toppings and
sauce at the ice cream store.
Chocolate
Vanilla
Strawberry
Mint
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot Fudge
Caramel
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
Caramel
Hot Fudge
CaramelHot Fudge
CaramelHot Fudge
Caramel
Each end “branch” represents one possible
outcome!
How many possible outcomes are there?
24 Total Outcomes!
Ice Cream:Chocolate
VanillaStrawberry
Mint
Toppings:Sprinkles PeanutsBananas
Sauce:Hot FudgeCaramel
Warren owns an Ice Cream Shop and had the sign below made to let people know what they can order:
Make a tree diagram to find all of the possible outcomes of ice cream, toppings and
sauce at the ice cream store.
Chocolate
Vanilla
Strawberry
Mint
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot Fudge
Caramel
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
Caramel
Hot Fudge
CaramelHot Fudge
CaramelHot Fudge
Caramel
What is the theoretical probability of a person
walking into the store and ordering: strawberry ice
cream, with bananas and hot fudge sauce?
1
24
Event Occurs
Total Outcomes
Ice Cream:Chocolate
VanillaStrawberry
Mint
Toppings:Sprinkles PeanutsBananas
Sauce:Hot FudgeCaramel
Warren owns an Ice Cream Shop and had the sign below made to let people know what they can order:
Make a tree diagram to find all of the possible outcomes of ice cream, toppings and
sauce at the ice cream store.
Chocolate
Vanilla
Strawberry
Mint
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot Fudge
Caramel
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
Caramel
Hot Fudge
CaramelHot Fudge
CaramelHot Fudge
Caramel
What is the theoretical probability of a person
walking into the store and order any type of ice
cream with sprinkles and caramel sauce?
4
24
Event Occurs
Total Outcomes
1
6
Ice Cream:Chocolate
VanillaStrawberry
Mint
Toppings:Sprinkles PeanutsBananas
Sauce:Hot FudgeCaramel
Warren owns an Ice Cream Shop and had the sign below made to let people know what they can order:
Make a tree diagram to find all of the possible outcomes of ice cream, toppings and
sauce at the ice cream store.
Chocolate
Vanilla
Strawberry
Mint
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Sprinkles
Peanuts
Bananas
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot FudgeCaramelHot Fudge
CaramelHot Fudge
Caramel
Hot Fudge
CaramelHot FudgeCaramelHot Fudge
Caramel
Hot Fudge
CaramelHot Fudge
CaramelHot Fudge
Caramel
What is the theoretical probability of a person
walking into the store and ordering vanilla ice cream with any kind of topping
and sauce?
6
24
Event Occurs
Total Outcomes
1
4
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Each end “branch” represents one possible outcome!
How many possible outcomes are there?
48 Total Outcomes!
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
What is the theoretical probability of Tina rolling a 5,
then spinning green and finally flipping tails?
1
48
Event Occurs
Total Outcomes
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
What is the theoretical probability of Tina flipping tails in
her experiment?
24
48
Event Occurs
Total Outcomes
1
2
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
What is the theoretical probability of Tina rolling an
even number, spinning blue and then flipping heads?
3
48
Event Occurs
Total Outcomes
1
16
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
What is the theoretical probability that Tina will roll a number greater than 1, spin a green or red, and finally flip
tails?
10
48
Event Occurs
Total Outcomes
5
24
Tina is performing an experiment where she is rolling a number cube, spinning a spinner
with 4 equal sections with the colors red, blue, yellow and green and then flipping
coin.
Blue
Yellow
Red
Green
Make a tree diagram to find all of the possible outcomes in this experiment.1
2
3
4
5
6
RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen
RedBlueYellowGreen
RedBlueYellowGreenRedBlueYellowGreen
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
TailsHeads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Heads
Tails
Tails
Tails
Tails
Tails
Tails
Tails
Tails
What is the theoretical probability that Tina will roll an
odd number on the number cube in her experiment?
24
48
Event Occurs
Total Outcomes
1
2
