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# # of combinations - PowerPoint PPT Presentation

By making a list, you know there are 6 combinations that include a jumbo drink. Same for large & medium. 6*3=18, so 18 possible outcomes. 3 sizes of drinks. # of combinations. Finding Sample Spaces with Tree Diagrams A sample space is a list of all possible outcomes of an experiment.

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By making a list, you know there are 6 combinations that include a jumbo drink. Same for large & medium.

6*3=18, so 18 possible outcomes

3 sizes of drinks

# of combinations

Finding Sample Spaces with Tree Diagrams include a jumbo drink. Same for large & medium.

Asample space is a list of all possible outcomes of an experiment.

If we rolled a die, the sample space would be 1,2,3,4,5, and 6.

How can we organize a sample space if more than one event occurs?

Tree Diagram include a jumbo drink. Same for large & medium.

Atree diagram is a organizational tool we can use to find a sample space.

Kardashian is going to have two children. What are all the possible  combinations of boys and girls she can get? (sample space)

What shall I wear? include a jumbo drink. Same for large & medium.

Jennifer has 3 skirts and 2 tops.

How many different outfits could she wear?

Make an organized list include a jumbo drink. Same for large & medium.

Skirt

Top

Red

Pink

Skirt

Top

Brown

Red

Red

Pink

Red

Brown

Blue

Pink

Blue

Pink

Blue

Brown

Blue

Brown

Green

Pink

Green

Pink

Green

Brown

Green

Brown

Make a tree diagram include a jumbo drink. Same for large & medium.

P

P

P

R

B

R

B

B

P

B

B

B

P

P

G

B

B

There are 6 outfit choices.

How many outfit choices now? include a jumbo drink. Same for large & medium.

Solution include a jumbo drink. Same for large & medium.

There are 12 outfit choices.

Calculating the total number of outcomes include a jumbo drink. Same for large & medium.

Find the total number of outcomes include a jumbo drink. Same for large & medium.

Flip a coin and roll a dice

6 x 2 = 12

Spin the spinner, roll a dice

6 x 8 = 48

Roll two six-sided dice

6 x 6 = 36

How many different dinner choices are there? include a jumbo drink. Same for large & medium.

Plates

Desserts

Sides

Onion Soup

Steak tips

Ice Cream

Canolis

Chicken Pie

French Fries

Lasagne

Cheeseburger

Burritos

You must choose 1 side, 1 plate and 1 dessert

3 x 5 x 2 = 30

Outcomes

H

T

You may not need

all the boxes!

Make a tree diagram and an organized list

Sample space coins?

Outcomes

H

H

T

H

T

T

4 (2 x 2)

How many possible outcomes are there?

How many outcomes include flipping at least one head?

3

What is the probability of flipping at least one head?

3

(0.75 or 75%)

4

Red

Blue

2

1

4

3

Green

Solution number?

1

1

2

2

4

3

Red

3

4

?

How many outcomes?

12

1

2

Blue

How many outcomes

with green and an odd

number?

?

2

3

4

1

Probability of green and

an odd number occurring?

2

Green

2

1

3

?

?

or

12

6

4

Independent events number?

2

1

4

3

No

If you spin a green on Spinner 1, does this affect what  you spin on Spinner 2?

Independent events: the outcome of one event does not  affect the outcome of another. If two events are independent,  to find the probability of them both occurring, multiply the  probabilities of the individual events occurring.

For example, probability of spinning a blue and spinning a 2:

1

4

1

12

1

P(Blue and 2) =

=

3

Flip a coin and roll a dice number?

What is the probability of flipping a tail and rolling a 5?

?

Total # outcomes

12

Click to reveal the total number of  outcomes and then use the Fill Tool  to shade the cells where the outcome  of the coin flip is a tail and the outcome of the dice roll is a 5.

=

P(Tail and 5) =

(

1

1

1

(

P(Tail and 5) =

12

2

6

Flip a coin and roll a dice number?

What is the probability of flipping a head and rolling a factor of 6?

?

Total # outcomes

12

Click to reveal the total number of  outcomes and then use the Fill Tool to  shade the cells where the outcome of  the coin flip is a head and the outcome of the dice roll is a factor of 6.

=

P(Head and Factor of 6) =

(

1

1

4

(

P (H and F6) =

3

2

6

Picking a ball from each jar number?

What's the probability of picking a red ball  from jar 1 and a green ball from jar 2?

1

1

1

2

=

=

4

5

10

2

What's the probability of picking a yellow  ball from jar 1 and a yellow ball from jar 2?

1

2

3

3

=

=

5

4

10

2

True or false? number?

The first four questions of the math test are "True/False"

type questions. Jason has not studied for the test and so he  guesses the answers. What is the probability he guesses the  correct answer for all four questions?

P(False) =

P(True) =

1

2

1

2

1

2

1

2

1

16

or 0.0625

=

What is the sample space, if we rolled the die and spun a spinner that  had the colors orange, purple, green and red?

http://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htmhttp://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

OUTCOMEhttp://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

FLAVOR

Set of all possible outcomes = sample space

ACG, AGC, CAG, CGA, GAC, GCA.

CONE

Outcome column shows sample space

3 types of crust

6 toppings

as a fractionhttp://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

as a percent

as a decimal

7-5http://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

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1http://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

2http://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm

3http://studyjams.scholastic.com/studyjams/jams/math/probability/tree-diagrams.htm