creating tree diagrams to find theoretical probability

Creating Tree Diagrams to find Theoretical Probability

We are learning to…find the theoretical probability of an event.

Saturday, April 22, 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

PeanutsBananas

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

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

PeanutsBananas

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

What is the theoretical probability of a person

walking into the store and ordering: strawberry ice

cream, with bananas and hot fudge sauce?

124

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

PeanutsBananas

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

What is the theoretical probability of a person

walking into the store and order any type of ice

cream with sprinkles and caramel sauce?

424

Event Occurs

Total Outcomes

16

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

PeanutsBananas

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

Hot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramelHot FudgeCaramel

What is the theoretical probability of a person

walking into the store and ordering vanilla ice cream with any kind of topping

and sauce?

624

Event Occurs

Total Outcomes

14

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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?

148

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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?

2448

Event Occurs

Total Outcomes

12

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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?

348

Event Occurs

Total Outcomes

116

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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?

1048

Event Occurs

Total Outcomes

524

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

RedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreenRedBlueYellowGreen

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

TailsHeads

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?

2448

Event Occurs

Total Outcomes

12