Creating Tree Diagrams to find Theoretical Probability
description
Transcript of 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