4.3 Tree Diagrams and Counting Techniques

[Pages:9]Prob & Stats

November 03, 2014

4.3 Tree Diagrams and Counting Techniques

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

Tree Diagram:

November 03, 2014

Used to model sample space or probability of a sequence of activities

Ex: tossing a coin and rolling a die

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

November 03, 2014

Create a tree diagram:

There are four blood types, A, B, AB and O. Blood can also be Rh+ and Rh. Finally, a blood donor can be classified as either male or female. How many different ways can a donor have his or her blood labeled?

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

Tree diagrams can also be used to calculate probability.

The twoway table shows the gender and handedness

of a class:

Female

Male

Righthanded 18

6

Lefthanded 3

1

Select two students at random

a) Draw a tree diagram that shows the sample space

b) Find the probability that both are lefthanded

November 03, 2014

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

November 03, 2014

Create a tree diagram and determine the probability for each outcome:

There are 5 marbles in a bag 3 are red, 2 are blue. You select one marble, note the color, set it aside, and then draw another.

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

Multiplication Rule of Counting

November 03, 2014

If there are n possible outcomes for event E1 and m possible outcomes for event E2, then there are a total of n x m or nm possible outcomes for the series of events E1 followed by E2

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

November 03, 2014

A paint manufacturer wants to manufacture several different paints. The categories include:

*Color: red, blue, white, black, green, brown, yellow

*Type: latex, oil

*Texture: flat, semigloss, high gloss

*Use: outdoor, indoor

How many different kinds of paint can be made if you can select one color, one type, one texture and one use?

4.3 Tree Diagrams & Counting Techniques

Prob & Stats

November 03, 2014

The manager of a department store wishes to make fourdigit ID cards for her employees. How many different cards can be made if she uses the digits 1, 2, 3, 4, 5, 6 and repetitions are permitted?

What if repetitions are not permitted?

4.3 Tree Diagrams & Counting Techniques

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