Bell WorkDetermine the total number of outcomes (combinations).

1) You are picking an outfit from the following list of clothes. If you choose one hat, one shirt, one pair of pants, and one pair of socks, how many total outfits could you make?Hats Shirts Pants Socks

BlueGreenYellow Black

PinkNeon GreenStriped

JeansCorduroys

Polk-a-dot“Bacon”Rainbow Toe-socks

Total Number of Hat Options: 4Total Number of Shirt Options: 3Total Number of Pants Options: 2Total Number of Socks Options: 3

4 x 3 x 2 x 3 =72

72 Outfits!

Tree Diagrams, Organized Lists, and Tables

Video

Tree Diagrams

•Way of organizing and visualizing outcomes

• Useful when the experiment happens in stages

• They can help you calculate probabilities

How many different ways can a red, blue and green marble be pulled from a

bag?

Solve using a Tree Diagram

How many different ways can a red, blue and green marble be pulled from a bag?

Chance Experiment:

Sample Space:

Total Number of Outcomes:

1

2

3

4

5

6

Pulling a Marble from a bag

Red, Blue, Green

6

How many different ways can a red, blue and green marble be pulled from a

bag?Try making an organized list

(R,B,G)(R,G, B)(G, R, B)(G, B, R)(B, G, R)(B, R, G)

HH HTTH TT

H TH

T

Making a TableYou flip a coin twice.

Make a table to display your outcome.

Why can’t we can’t we use this method for the problem where we draw marbles out of a bag?

What is the probability of getting green, blue and red in that order?

P(g, b, r)=

Independent and Dependent EventsTell whether the events are independent or dependent.

You randomly draw a number from a bag. Then you randomly draw a second number without putting the first number back.

b.

You roll a number cube. Then you roll the number cube again.

a.

The result of the first roll does not affect the result of the second roll, so the events are independent.

There is one fewer number in the bag for the second draw, so the events are dependent.

You TryIn Exercises 1 and 2, tell whether the events are

independent or dependent. Explain your reasoning.

1. You toss a coin. Then you roll a number cube.

You randomly choose 1 of 10 marbles. Then you randomly choose one of the remaining 9 marbles.

2.

The coins toss does not affect the roll of a dice, so the events are independent.

There is one fewer number in the bag for the second draw, so the events are dependent.

1 1P(head and tail)

21

=2 4

x

1 1P(tail and tail)

21

=2 4

x

12

head

tail

First Coin Second Coin

head

tail

head

tail

12

12

12

12

12

1 1P(head and head)

21

=2 4

x

1 1P(tail and head)

21

=2 4

x

Peter tosses two coins.

(a)Draw a tree diagram to show all possible outcomes.

(b) Use your tree diagram to find the probability of getting

(i) 2 Heads

(ii) A head or a tail in any order.

P(2 heads) = ¼

P(head and a tail or a tail and a head) = ½

Independent Events

2 Independent

Events.

3 Selections

710

310

First Draw Second Draw

red

red

blue

red

red

red

red

blue

blue

blue

blue

red

blue

blue

Third Draw

You choose a colored chip and then replace it. Finish the tree diagram for the second and third draw.

310

310

710310

710

710

310

710

310

710 3

10

710

Practice